2.1 Övningar

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Rad 1: Rad 1:
 +__NOTOC__
==Övning 2.1:1== ==Övning 2.1:1==
<div class="ovning"> <div class="ovning">
Utveckla Utveckla
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">a) </td>+<td class="ntext">a)</td>
-<td class="ntext">$3x(x-1)$</td>+<td class="ntext" width="33%">$3x(x-1)$</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">$(1+x-x^2)xy$</td>+<td class="ntext" width="33%">$(1+x-x^2)xy$</td>
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">$-x^2(4-y^2)$</td>+<td class="ntext" width="33%">$-x^2(4-y^2)$</td>
-<td class="ntext">d)</td>+
-<td class="ntext">$x^3y^2\left(\displaystyle \frac{1}{y} - \frac{1}{xy}+1\right)$</td>+
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
 +<td class="ntext">d)</td>
 +<td class="ntext" width="33%">$x^3y^2\left(\displaystyle \frac{1}{y} - \frac{1}{xy}+1\right)$</td>
<td class="ntext">e) </td> <td class="ntext">e) </td>
-<td class="ntext">$(x-7)^2$</td>+<td class="ntext" width="33%">$(x-7)^2$</td>
<td class="ntext">f)</td> <td class="ntext">f)</td>
-<td class="ntext">$(5+4y)^2$</td>+<td class="ntext" width="33%">$(5+4y)^2$</td>
 +</tr>
 +<tr align="left">
<td class="ntext">g)</td> <td class="ntext">g)</td>
-<td class="ntext">$(y^2-3x^3)^2$</td>+<td class="ntext" width="33%">$(y^2-3x^3)^2$</td>
<td class="ntext">h)</td> <td class="ntext">h)</td>
-<td class="ntext">$(5x^3+3x^5)^2$</td>+<td class="ntext" width="33%">$(5x^3+3x^5)^2$</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 32: Rad 33:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Facit till alla delfrågorna<br \>+Facit till alla delfrågor
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">a) </td>+<td class="ntext">a)</td>
-<td class="ntext">$3x^2-3x$</td>+<td class="ntext" width="33%">$3x^2-3x$</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">$xy+x^2y-x^3y$</td>+<td class="ntext" width="33%">$xy+x^2y-x^3y$</td>
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">$-4x^2+x^2y^2$</td>+<td class="ntext" width="33%">$-4x^2+x^2y^2$</td>
-<td class="ntext">d)</td>+
-<td class="ntext">$x^3y-x^2y+x^3y^2$</td>+
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">e) </td>+<td class="ntext">d)</td>
-<td class="ntext">$x^2-14x+49$</td>+<td class="ntext" width="33%">$x^3y-x^2y+x^3y^2$</td>
 +<td class="ntext">e)</td>
 +<td class="ntext" width="33%">$x^2-14x+49$</td>
<td class="ntext">f)</td> <td class="ntext">f)</td>
-<td class="ntext">$16y^2+40y+25$</td>+<td class="ntext" width="33%">$16y^2+40y+25$</td>
 +</tr>
 +<tr align="left">
<td class="ntext">g)</td> <td class="ntext">g)</td>
-<td class="ntext">$9x^6-6x^3y^2+y^4$</td>+<td class="ntext" width="33%">$9x^6-6x^3y^2+y^4$</td>
<td class="ntext">h)</td> <td class="ntext">h)</td>
-<td class="ntext">$9x^{10}+30x^8+25x^6$</td>+<td class="ntext" width="33%">$9x^{10}+30x^8+25x^6$</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 62: Rad 63:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a<br />[[Bild:2_1_1a.gif]]+Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_1a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</DIV>+<div class=NavHead>L&ouml;sning b)&nbsp;</DIV>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b<br />[[Bild:2_1_1b.gif]]+Lösning till delfråga b)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_1b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c<br />[[Bild:2_1_1c.gif]]+Lösning till delfråga c)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_1c.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning d&nbsp;</DIV>+<div class=NavHead>L&ouml;sning d)&nbsp;</DIV>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga d<br />[[Bild:2_1_1d.gif]]+Lösning till delfråga d)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_1d.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning e&nbsp;</div>+<div class=NavHead>L&ouml;sning e)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga e<br />[[Bild:2_1_1e.gif]]+Lösning till delfråga e)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_1e.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning f&nbsp;</DIV>+<div class=NavHead>L&ouml;sning f)&nbsp;</DIV>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga f<br />[[Bild:2_1_1f.gif]]+Lösning till delfråga f)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_1f.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning g&nbsp;</div>+<div class=NavHead>L&ouml;sning g)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga g<br />[[Bild:2_1_1g.gif]]+Lösning till delfråga g)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_1g.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning h&nbsp;</DIV>+<div class=NavHead>L&ouml;sning h)&nbsp;</DIV>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga h<br />[[Bild:2_1_1h.gif]]+Lösning till delfråga h)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_1h.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
-==Övning 2.2:2==+==Övning 2.1:2==
<div class="ovning"> <div class="ovning">
Utveckla och förenkla så långt som möjligt Utveckla och förenkla så långt som möjligt
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">$(x-4)(x-5)-3x(2x-3)$</td>+<td class="ntext" width="50%">$(x-4)(x-5)-3x(2x-3)$</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">$(1-5x)(1+15x)-3(2-5x)(2+5x)$</td>+<td class="ntext" width="50%">$(1-5x)(1+15x)-3(2-5x)(2+5x)$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">$(3x+4)^2-(3x-2)(3x-8)$</td>+<td class="ntext" width="50%">$(3x+4)^2-(3x-2)(3x-8)$</td>
<td class="ntext">d)</td> <td class="ntext">d)</td>
-<td class="ntext">$(3x^2+2)(3x^2-2)(9x^4+4)$</td>+<td class="ntext" width="50%">$(3x^2+2)(3x^2-2)(9x^4+4)$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">e)</td> <td class="ntext">e)</td>
-<td class="ntext">$(a+b)^2+(a-b)^2$</td>+<td class="ntext" width="50%">$(a+b)^2+(a-b)^2$</td>
-<td class="ntext"></td>+
-<td class="ntext"></td>+
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 149: Rad 201:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Facit till alla delfrågorna<br \>+Facit till alla delfrågor<br \>
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">$-5^2+20$</td>+<td class="ntext" width="50%">$-5x^2+20$</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">$-11+10x$</td>+<td class="ntext" width="50%">$10x-11$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">$54x$</td>+<td class="ntext" width="50%">$54x$</td>
<td class="ntext">d)</td> <td class="ntext">d)</td>
-<td class="ntext">$81x^8-16$</td>+<td class="ntext" width="50%">$81x^8-16$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">e)</td> <td class="ntext">e)</td>
-<td class="ntext">$2a^2+2b^2$</td>+<td class="ntext" width="50%">$2a^2+2b^2$</td>
-<td class="ntext"></td>+
-<td class="ntext"></td>+
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 178: Rad 225:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a <br \>[[Bild:2_1_2a.gif]]+Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_2a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 186: Rad 240:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b <br \>[[Bild:2_1_2b.gif]]+Lösning till delfråga b)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_2b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
 +
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c <br \>[[Bild:2_1_2c.gif]]+Lösning till delfråga c)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_2c.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
 +
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga d <br \>[[Bild:2_1_2d.gif]]+Lösning till delfråga d)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_2d.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
 +
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning e&nbsp;</div>+<div class=NavHead>L&ouml;sning e)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga e <br \>[[Bild:2_1_2e.gif]]+Lösning till delfråga e)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_2e.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 216: Rad 301:
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{a) }$</td>+<td class="ntext">a)</td>
-<td class="ntext"> $x^2-36$</td>+<td class="ntext" width="33%">$x^2-36$</td>
-<td class="ntext">$\textrm{b) }$</td>+<td class="ntext">b)</td>
-<td class="ntext">$5x^2-20$</td>+<td class="ntext" width="33%">$5x^2-20$</td>
 +<td class="ntext">c)</td>
 +<td class="ntext" width="33%">$x^2+6x+9$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{c) }$</td>+<td class="ntext">d)</td>
-<td class="ntext">$x^2+6x+9$</td>+<td class="ntext" width="33%">$x^2-10x+25$</td>
-<td class="ntext">$\textrm{d) }$</td>+<td class="ntext">e)</td>
-<td class="ntext">$x^2-10x+25$</td>+<td class="ntext" width="33%">$18x-2x^3$</td>
-</tr>+<td class="ntext">f)</td>
-<tr><td height="5px"/></tr>+<td class="ntext" width="33%">$16x^2+8x+1$</td>
-<tr align="left">+
-<td class="ntext">$\textrm{e) }$</td>+
-<td class="ntext">$18x-2x^3$</td>+
-<td class="ntext">$\textrm{f) }$</td>+
-<td class="ntext">$16x^2+8x+1$</td>+
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 242: Rad 323:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Facit till alla delfrågorna<br \>+Facit till alla delfrågor
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{a) }$</td>+<td class="ntext">a)</td>
-<td class="ntext"> $(x+6)(x-6)$</td>+<td class="ntext" width="33%">$(x+6)(x-6)$</td>
-<td class="ntext">$\textrm{b) }$</td>+<td class="ntext">b)</td>
-<td class="ntext">$5(x+2)(x-2)$</td>+<td class="ntext" width="33%">$5(x+2)(x-2)$</td>
 +<td class="ntext">c)</td>
 +<td class="ntext" width="33%">$(x+3)^2$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{c) }$</td>+<td class="ntext">d)</td>
-<td class="ntext">$(x+3)^2$</td>+<td class="ntext" width="33%">$(x-5)^2$</td>
-<td class="ntext">$\textrm{d) }$</td>+<td class="ntext">e)</td>
-<td class="ntext">$(x-5)^2$</td>+<td class="ntext" width="33%">$-2x(x+3)(x-3)$</td>
-</tr>+<td class="ntext">f)</td>
-<tr><td height="5px"/></tr>+<td class="ntext" width="33%">$(4x+1)^2$</td>
-<tr align="left">+
-<td class="ntext">$\textrm{e) }$</td>+
-<td class="ntext">$-2x(x+3)(x-3)$</td>+
-<td class="ntext">$\textrm{f) }$</td>+
-<td class="ntext">$(4x+1)^2$</td>+
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
</table> </table>
- 
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a<br \>[[Bild:2_1_3a.gif]]+Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_3a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b<br \>[[Bild:2_1_3b.gif]]+Lösning till delfråga b)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_3b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c<br \>[[Bild:2_1_3c.gif]]+Lösning till delfråga c)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_3c.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga d<br \>[[Bild:2_1_3d.gif]]+Lösning till delfråga d)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_3d.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning e&nbsp;</div>+<div class=NavHead>L&ouml;sning e)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga e<br \>[[Bild:2_1_3e.gif]]+Lösning till delfråga e)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_3e.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning f&nbsp;</div>+<div class=NavHead>L&ouml;sning f)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga f<br \>[[Bild:2_1_3f.gif]]+Lösning till delfråga f)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_3f.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 314: Rad 432:
==Övning 2.1:4== ==Övning 2.1:4==
<div class="ovning"> <div class="ovning">
-Bestäm koefficienterna framför $x$ och $x^2$ när följande uttryck utvecklas+Bestäm koefficienterna framför $\,x\,$ och $\,x^2\,$ när följande uttryck utvecklas
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">$(x+2)(3x^2-x+5)$</td>+<td class="ntext" width="100%">$(x+2)(3x^2-x+5)$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">$(1+x+x^2+x^3)(2-x+x^2+x^4)$</td>+<td class="ntext" width="100%">$(1+x+x^2+x^3)(2-x+x^2+x^4)$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">$(x-x^3+x^5)(1+3x+5x^2)(2-7x^2-x^4)$</td>+<td class="ntext" width="100%">$(x-x^3+x^5)(1+3x+5x^2)(2-7x^2-x^4)$</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 337: Rad 453:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Facit till alla delfrågorna <br \>+Facit till alla delfrågor
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">$5$ framf&ouml;r $x^2$, $3$ framf&ouml;r $x$</td>+<td class="ntext" width="100%">$5\,$ framf&ouml;r $\,x^2\,$, $\,3\,$ framf&ouml;r $\,x$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">$2$ framf&ouml;r $x^2$, $1$ framf&ouml;r $x$</td>+<td class="ntext" width="100%">$2\,$ framf&ouml;r $\,x^2\,$, $\,1\,$ framf&ouml;r $\,x$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">$\textrm{c) }$</td> <td class="ntext">$\textrm{c) }$</td>
-<td class="ntext">$6$ framf&ouml;r $x^2$, $2$ framf&ouml;r $x$</td>+<td class="ntext" width="100%">$6\,$ framf&ouml;r $\,x^2\,$, $\,2\,$ framf&ouml;r $\,x$</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 359: Rad 473:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning &nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga <br \>[[Bild:2_1_4a.gif]]+Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_4a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning &nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga <br \>[[Bild:2_1_4b-1(2).gif]]<br \>[[Bild:2_1_4b-2(2).gif]]+Lösning till delfråga b)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_4b-1(2).gif]]
 +</td>
 +</tr>
 +<tr>
 +<td align="center">
 +[[Bild:2_1_4b-2(2).gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning &nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga <br \>[[Bild:2_1_4c.gif]]+Lösning till delfråga c)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_4c.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 384: Rad 524:
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{a) }$</td>+<td class="ntext">a)</td>
-<td class="ntext">$\displaystyle \frac{1}{x-x^2}-\displaystyle \frac{1}{x}$</td>+<td class="ntext" width="50%">$\displaystyle \frac{1}{x-x^2}-\displaystyle \frac{1}{x}$</td>
-<td class="ntext">$\textrm{b) }$</td>+<td class="ntext">b)</td>
-<td class="ntext">$\displaystyle \frac{1}{y^2-2y}-\displaystyle \frac{2}{y^2-4}$</td>+<td class="ntext" width="50%">$\displaystyle \frac{1}{y^2-2y}-\displaystyle \frac{2}{y^2-4}$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
-<td class="ntext">$\textrm{c) }$</td>+<td class="ntext">c)</td>
-<td class="ntext">$\displaystyle \frac{(3x^2-12)(x^2-1)}{(x+1)(x+2)}$</td>+<td class="ntext" width="50%">$\displaystyle \frac{(3x^2-12)(x^2-1)}{(x+1)(x+2)}$</td>
-<td class="ntext">$\textrm{d) }$</td>+<td class="ntext">d)</td>
-<td class="ntext">$\displaystyle \frac{(y^2+4y+4)(2y-4)}{(y^2+4)(y^2-4)}$</td>+<td class="ntext" width="50%">$\displaystyle \frac{(y^2+4y+4)(2y-4)}{(y^2+4)(y^2-4)}$</td>
</tr> </tr>
</table> </table>
Rad 402: Rad 541:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Facit till alla delfrågorna<br \>+Facit till alla delfrågor
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
<tr align="left"> <tr align="left">
- 
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">$\displaystyle \frac{1}{1-x}$</td>+<td class="ntext" width="50%">$\displaystyle \frac{1}{1-x}$</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">$-\displaystyle \frac{1}{y(y+2)}$</td>+<td class="ntext" width="50%">$-\displaystyle \frac{1}{y(y+2)}$</td>
</tr> </tr>
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">$3(x-2)(x-1)$</td>+<td class="ntext" width="50%">$3(x-2)(x-1)$</td>
<td class="ntext">d)</td> <td class="ntext">d)</td>
-<td class="ntext">$\displaystyle \frac{2(y+2)}{y^2+4}$</td>+<td class="ntext" width="50%">$\displaystyle \frac{2(y+2)}{y^2+4}$</td>
</tr> </tr>
</table> </table>
- 
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a<br \>[[Bild:2_1_5a.gif]]+Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_5a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b<br \>[[Bild:2_1_5b.gif]]+Lösning till delfråga b)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_5b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c<br \>[[Bild:2_1_5c.gif]]+Lösning till delfråga c)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_5c.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga d<br \>[[Bild:2_1_5d-1(2).gif]]<br \>[[Bild:2_1_5d-2(2).gif]]+Lösning till delfråga d)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_5d-1(2).gif]]
 +</td>
 +</tr>
 +<tr>
 +<td align="center">
 +[[Bild:2_1_5d-2(2).gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 453: Rad 622:
==Övning 2.1:6== ==Övning 2.1:6==
<div class="ovning"> <div class="ovning">
 +Förenkla så långt som möjligt
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">$\left(x-y+\displaystyle\frac{x^2}{y-x}\right)$ $\left(\displaystyle\frac{y}{2x-y}-1\right)$</td>+<td class="ntext" width="50%">$\left(x-y+\displaystyle\frac{x^2}{y-x}\right)$ $\left(\displaystyle\frac{y}{2x-y}-1\right)$</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">$\displaystyle \frac{x}{x-2}+\displaystyle \frac{x}{x+3}-2$</td>+<td class="ntext" width="50%">$\displaystyle \frac{x}{x-2}+\displaystyle \frac{x}{x+3}-2$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">$\displaystyle \frac{2a+b}{a^2-ab}-\frac{2}{a-b}$</td>+<td class="ntext" width="50%">$\displaystyle \frac{2a+b}{a^2-ab}-\frac{2}{a-b}$</td>
<td class="ntext">d)</td> <td class="ntext">d)</td>
-<td class="ntext">$\displaystyle\frac{a-b+\displaystyle\frac{b^2}{a+b}}{1-\left(\displaystyle\frac{a-b}{a+b}\right)^2}$</td>+<td class="ntext" width="50%">$\displaystyle\frac{a-b+\displaystyle\frac{b^2}{a+b}}{1-\left(\displaystyle\frac{a-b}{a+b}\right)^2}$</td>
</tr> </tr>
 +<tr><td height="5px"/></tr>
</table> </table>
</div> </div>
- 
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Facit till alla delfrågorna<br \>+Facit till alla delfrågor<br \>
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">$2y$</td>+<td class="ntext" width="50%">$2y$</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">$\displaystyle\frac{-x+12}{(x-2)(x+3)}$</td>+<td class="ntext" width="50%">$\displaystyle\frac{-x+12}{(x-2)(x+3)}$</td>
</tr> </tr>
<tr align="left"> <tr align="left">
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">$\displaystyle\frac{b}{a(a-b)}$</td>+<td class="ntext" width="50%">$\displaystyle\frac{b}{a(a-b)}$</td>
<td class="ntext">d)</td> <td class="ntext">d)</td>
-<td class="ntext">$\displaystyle\frac{a(a+b)}{4b}$</td>+<td class="ntext" width="50%">$\displaystyle\frac{a(a+b)}{4b}$</td>
</tr> </tr>
</table> </table>
Rad 492: Rad 662:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a<br \>[[Bild:2_1_6a.gif]]+Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_6a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b<br \>[[Bild:2_1_6b.gif]]+Lösning till delfråga b)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_6b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c<br \>[[Bild:2_1_6c.gif]]+Lösning till delfråga c)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_6c.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga d<br \>[[Bild:2_1_6d.gif]]+Lösning till delfråga d)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_6d.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 523: Rad 721:
Förenkla följande bråkuttryck genom att skriva på gemensamt bråkstreck Förenkla följande bråkuttryck genom att skriva på gemensamt bråkstreck
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">$\displaystyle \frac{2}{x+3}-\frac{2}{x+5}$</td>+<td class="ntext" width="33%">$\displaystyle \frac{2}{x+3}-\frac{2}{x+5}$</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">$x+\displaystyle \frac{1}{x-1}+\displaystyle \frac{1}{x^2}$</td>+<td class="ntext" width="33%">$x+\displaystyle \frac{1}{x-1}+\displaystyle \frac{1}{x^2}$</td>
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">$\displaystyle \frac{ax}{a+1}-\displaystyle \frac{ax^2}{(a+1)^2}$</td>+<td class="ntext" width="33%">$\displaystyle \frac{ax}{a+1}-\displaystyle \frac{ax^2}{(a+1)^2}$</td>
</tr> </tr>
</table> </table>
Rad 540: Rad 737:
Facit till alla delfrågorna<br \> Facit till alla delfrågorna<br \>
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">$\displaystyle \frac{4}{(x+3)(x+5)}$</td>+<td class="ntext" width="33%">$\displaystyle \frac{4}{(x+3)(x+5)}$</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">$\displaystyle \frac{x^4-x^3+x^2+x-1}{x^2(x+1)}$</td>+<td class="ntext" width="33%">$\displaystyle \frac{x^4-x^3+x^2+x-1}{x^2(x-1)}$</td>
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">$\displaystyle \frac{ax-ax^2}{a+1}$</td>+<td class="ntext" width="33%">$\displaystyle \frac{ax(a+1-x)}{(a+1)^2}$</td>
</tr> </tr>
</table> </table>
Rad 554: Rad 750:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a<br \>[[Bild:2_1_7a.gif]]+Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_7a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b<br \>[[Bild:2_1_7b.gif]]+Lösning till delfråga b)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_7b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c<br \>[[Bild:2_1_7c.gif]]+Lösning till delfråga c)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_7c.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
Rad 577: Rad 794:
<div class="ovning"> <div class="ovning">
 +Förenkla följande bråkuttryck genom att skriva på gemensamt bråkstreck
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr> <tr>
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">$\displaystyle \frac{\displaystyle \frac{x}{x+1}}{3+x}$</td>+<td class="ntext" width="33%">$\displaystyle \frac{\displaystyle\ \frac{x}{x+1}\ }{\ 3+x\ }$</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">$\displaystyle \frac{\displaystyle \frac{3}{x}-\displaystyle \frac{1}{x}}{\displaystyle \frac{1}{x-3}}$</td>+<td class="ntext" width="33%">$\displaystyle \frac{\displaystyle \frac{3}{x}-\displaystyle \frac{1}{x}}{\displaystyle \frac{1}{x-3}}$</td>
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">$\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+x}}}$</td>+<td class="ntext" width="33%">$\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+x}}}$</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 594: Rad 811:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Facit till alla delfrågorna<br \>+Facit till alla delfrågor<br \>
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
-<tr><td height="5px"/></tr> 
<tr align="left"> <tr align="left">
<td class="ntext">a)</td> <td class="ntext">a)</td>
-<td class="ntext">$\displaystyle \frac{x}{(x+3)(x+1)}$</td>+<td class="ntext" width="33%">$\displaystyle \frac{x}{(x+3)(x+1)}$</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">$\displaystyle \frac{2(x-3)}{x}$</td>+<td class="ntext" width="33%">$\displaystyle \frac{2(x-3)}{x}$</td>
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">$\displaystyle \frac{x+2}{2x+3}$</td>+<td class="ntext" width="33%">$\displaystyle \frac{x+2}{2x+3}$</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 611: Rad 827:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga a<br \>[[Bild:2_1_8a.gif]]+Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_8a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga b<br \>[[Bild:2_1_8b.gif]]+Lösning till delfråga b)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_8b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</div>
<div class=NavContent> <div class=NavContent>
-Lösning till delfråga c<br \>[[Bild:2_1_8c-1(2).gif]]<br \>[[Bild:2_1_8c-2(2).gif]]+Lösning till delfråga c)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:2_1_8c-1(2).gif]]
 +</td>
 +</tr>
 +<tr>
 +<td align="center">
 +[[Bild:2_1_8c-2(2).gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>

Versionen från 13 maj 2007 kl. 10.01

Övning 2.1:1

Utveckla

a) $3x(x-1)$ b) $(1+x-x^2)xy$ c) $-x^2(4-y^2)$
d) $x^3y^2\left(\displaystyle \frac{1}{y} - \frac{1}{xy}+1\right)$ e) $(x-7)^2$ f) $(5+4y)^2$
g) $(y^2-3x^3)^2$ h) $(5x^3+3x^5)^2$

Övning 2.1:2

Utveckla och förenkla så långt som möjligt

a) $(x-4)(x-5)-3x(2x-3)$ b) $(1-5x)(1+15x)-3(2-5x)(2+5x)$
c) $(3x+4)^2-(3x-2)(3x-8)$ d) $(3x^2+2)(3x^2-2)(9x^4+4)$
e) $(a+b)^2+(a-b)^2$


Övning 2.1:3

Faktorisera så långt som möjligt

a) $x^2-36$ b) $5x^2-20$ c) $x^2+6x+9$
d) $x^2-10x+25$ e) $18x-2x^3$ f) $16x^2+8x+1$

Övning 2.1:4

Bestäm koefficienterna framför $\,x\,$ och $\,x^2\,$ när följande uttryck utvecklas

a) $(x+2)(3x^2-x+5)$
b) $(1+x+x^2+x^3)(2-x+x^2+x^4)$
c) $(x-x^3+x^5)(1+3x+5x^2)(2-7x^2-x^4)$

Övning 2.1:5

Förenkla så långt som möjligt

a) $\displaystyle \frac{1}{x-x^2}-\displaystyle \frac{1}{x}$ b) $\displaystyle \frac{1}{y^2-2y}-\displaystyle \frac{2}{y^2-4}$
c) $\displaystyle \frac{(3x^2-12)(x^2-1)}{(x+1)(x+2)}$ d) $\displaystyle \frac{(y^2+4y+4)(2y-4)}{(y^2+4)(y^2-4)}$

Övning 2.1:6

Förenkla så långt som möjligt

a) $\left(x-y+\displaystyle\frac{x^2}{y-x}\right)$ $\left(\displaystyle\frac{y}{2x-y}-1\right)$ b) $\displaystyle \frac{x}{x-2}+\displaystyle \frac{x}{x+3}-2$
c) $\displaystyle \frac{2a+b}{a^2-ab}-\frac{2}{a-b}$ d) $\displaystyle\frac{a-b+\displaystyle\frac{b^2}{a+b}}{1-\left(\displaystyle\frac{a-b}{a+b}\right)^2}$

Övning 2.1:7

Förenkla följande bråkuttryck genom att skriva på gemensamt bråkstreck

a) $\displaystyle \frac{2}{x+3}-\frac{2}{x+5}$ b) $x+\displaystyle \frac{1}{x-1}+\displaystyle \frac{1}{x^2}$ c) $\displaystyle \frac{ax}{a+1}-\displaystyle \frac{ax^2}{(a+1)^2}$

Övning 2.1:8

Förenkla följande bråkuttryck genom att skriva på gemensamt bråkstreck

a) $\displaystyle \frac{\displaystyle\ \frac{x}{x+1}\ }{\ 3+x\ }$ b) $\displaystyle \frac{\displaystyle \frac{3}{x}-\displaystyle \frac{1}{x}}{\displaystyle \frac{1}{x-3}}$ c) $\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+x}}}$
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