Versionen från 21 juni 2007 kl. 14.26 (redigera) KTH.SE:u1xsetv1 (Diskussion | bidrag) ← Gå till föregående ändring |
Versionen från 21 juni 2007 kl. 14.29 (redigera) (ogör) KTH.SE:u1xsetv1 (Diskussion | bidrag)
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Rad 693: |
Rad 693: |
| <td class="ntext">f)</td> | | <td class="ntext">f)</td> |
| <td class="ntext" width="33%">3^{40}>2^{56}</td> | | <td class="ntext" width="33%">3^{40}>2^{56}</td> |
| + | </tr> |
| + | <tr><td height="5px"/></tr> |
| + | </table> |
| + | </div> |
| + | |
| + | ==Övning 2.1:1== |
| + | <div class="ovning"> |
| + | Utveckla |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr align="left"> |
| + | <td class="ntext">a)</td> |
| + | <td class="ntext" width="33%">3x(x-1)</td> |
| + | <td class="ntext">b)</td> |
| + | <td class="ntext" width="33%">(1+x-x^2)xy</td> |
| + | <td class="ntext">c)</td> |
| + | <td class="ntext" width="33%">-x^2(4-y^2)</td> |
| + | </tr> |
| + | <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" width="33%">(x-7)^2</td> |
| + | <td class="ntext">f)</td> |
| + | <td class="ntext" width="33%">(5+4y)^2</td> |
| + | </tr> |
| + | <tr align="left"> |
| + | <td class="ntext">g)</td> |
| + | <td class="ntext" width="33%">(y^2-3x^3)^2</td> |
| + | <td class="ntext">h)</td> |
| + | <td class="ntext" width="33%">(5x^3+3x^5)^2</td> |
| + | </tr> |
| + | <tr><td height="5px"/></tr> |
| + | </table> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Facit </div> |
| + | <div class=NavContent> |
| + | Facit till alla delfrågor |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr align="left"> |
| + | <td class="ntext">a)</td> |
| + | <td class="ntext" width="33%">3x^2-3x</td> |
| + | <td class="ntext">b)</td> |
| + | <td class="ntext" width="33%">xy+x^2y-x^3y</td> |
| + | <td class="ntext">c)</td> |
| + | <td class="ntext" width="33%">-4x^2+x^2y^2</td> |
| + | </tr> |
| + | <tr align="left"> |
| + | <td class="ntext">d)</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" width="33%">16y^2+40y+25</td> |
| + | </tr> |
| + | <tr align="left"> |
| + | <td class="ntext">g)</td> |
| + | <td class="ntext" width="33%">9x^6-6x^3y^2+y^4</td> |
| + | <td class="ntext">h)</td> |
| + | <td class="ntext" width="33%">9x^{10}+30x^8+25x^6</td> |
| + | </tr> |
| + | <tr><td height="5px"/></tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning a) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_1a.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning b) </DIV> |
| + | <div class=NavContent> |
| + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_1b.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning c) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_1c.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning d) </DIV> |
| + | <div class=NavContent> |
| + | Lösning till delfråga d) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_1d.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning e) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga e) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_1e.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning f) </DIV> |
| + | <div class=NavContent> |
| + | Lösning till delfråga f) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_1f.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning g) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga g) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_1g.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning h) </DIV> |
| + | <div class=NavContent> |
| + | Lösning till delfråga h) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_1h.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | ==Övning 2.1:2== |
| + | <div class="ovning"> |
| + | Utveckla och förenkla så långt som möjligt |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr align="left"> |
| + | <td class="ntext">a)</td> |
| + | <td class="ntext" width="50%">(x-4)(x-5)-3x(2x-3)</td> |
| + | <td class="ntext">b)</td> |
| + | <td class="ntext" width="50%">(1-5x)(1+15x)-3(2-5x)(2+5x)</td> |
| + | </tr> |
| + | <tr align="left"> |
| + | <td class="ntext">c)</td> |
| + | <td class="ntext" width="50%">(3x+4)^2-(3x-2)(3x-8)</td> |
| + | <td class="ntext">d)</td> |
| + | <td class="ntext" width="50%">(3x^2+2)(3x^2-2)(9x^4+4)</td> |
| + | </tr> |
| + | <tr align="left"> |
| + | <td class="ntext">e)</td> |
| + | <td class="ntext" width="50%">(a+b)^2+(a-b)^2</td> |
| + | </tr> |
| + | <tr><td height="5px"/></tr> |
| + | </table> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Facit </div> |
| + | <div class=NavContent> |
| + | Facit till alla delfrågor<br \> |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr align="left"> |
| + | <td class="ntext">a)</td> |
| + | <td class="ntext" width="50%">-5x^2+20</td> |
| + | <td class="ntext">b)</td> |
| + | <td class="ntext" width="50%">10x-11</td> |
| + | </tr> |
| + | <tr align="left"> |
| + | <td class="ntext">c)</td> |
| + | <td class="ntext" width="50%">54x</td> |
| + | <td class="ntext">d)</td> |
| + | <td class="ntext" width="50%">81x^8-16</td> |
| + | </tr> |
| + | <tr align="left"> |
| + | <td class="ntext">e)</td> |
| + | <td class="ntext" width="50%">2a^2+2b^2</td> |
| + | </tr> |
| + | <tr><td height="5px"/></tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning a) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_2a.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning b) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_2b.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning c) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_2c.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning d) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga d) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_2d.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning e) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga e) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_2e.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | ==Övning 2.1:3== |
| + | |
| + | <div class="ovning"> |
| + | Faktorisera så långt som möjligt |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr align="left"> |
| + | <td class="ntext">a)</td> |
| + | <td class="ntext" width="33%">x^2-36</td> |
| + | <td class="ntext">b)</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 align="left"> |
| + | <td class="ntext">d)</td> |
| + | <td class="ntext" width="33%">x^2-10x+25</td> |
| + | <td class="ntext">e)</td> |
| + | <td class="ntext" width="33%">18x-2x^3</td> |
| + | <td class="ntext">f)</td> |
| + | <td class="ntext" width="33%">16x^2+8x+1</td> |
| + | </tr> |
| + | <tr><td height="5px"/></tr> |
| + | </table> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Facit </div> |
| + | <div class=NavContent> |
| + | Facit till alla delfrågor |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr align="left"> |
| + | <td class="ntext">a)</td> |
| + | <td class="ntext" width="33%">(x+6)(x-6)</td> |
| + | <td class="ntext">b)</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 align="left"> |
| + | <td class="ntext">d)</td> |
| + | <td class="ntext" width="33%">(x-5)^2</td> |
| + | <td class="ntext">e)</td> |
| + | <td class="ntext" width="33%">-2x(x+3)(x-3)</td> |
| + | <td class="ntext">f)</td> |
| + | <td class="ntext" width="33%">(4x+1)^2</td> |
| + | </tr> |
| + | <tr><td height="5px"/></tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning a) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_3a.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning b) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_3b.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning c) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_3c.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning d) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga d) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_3d.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning e) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga e) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_3e.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning f) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga f) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_3f.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | ==Övning 2.1:4== |
| + | <div class="ovning"> |
| + | Bestäm koefficienterna framför \,x\, och \,x^2\, när följande uttryck utvecklas |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr align="left"> |
| + | <td class="ntext">a)</td> |
| + | <td class="ntext" width="100%">(x+2)(3x^2-x+5)</td> |
| + | </tr> |
| + | <tr align="left"> |
| + | <td class="ntext">b)</td> |
| + | <td class="ntext" width="100%">(1+x+x^2+x^3)(2-x+x^2+x^4)</td> |
| + | </tr> |
| + | <tr align="left"> |
| + | <td class="ntext">c)</td> |
| + | <td class="ntext" width="100%">(x-x^3+x^5)(1+3x+5x^2)(2-7x^2-x^4)</td> |
| + | </tr> |
| + | <tr><td height="5px"/></tr> |
| + | </table> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Facit </div> |
| + | <div class=NavContent> |
| + | Facit till alla delfrågor |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr align="left"> |
| + | <td class="ntext">a)</td> |
| + | <td class="ntext" width="100%">5\, framför \,x^2\,, \,3\, framför \,x</td> |
| + | </tr> |
| + | <tr align="left"> |
| + | <td class="ntext">b)</td> |
| + | <td class="ntext" width="100%">2\, framför \,x^2\,, \,1\, framför \,x</td> |
| + | </tr> |
| + | <tr align="left"> |
| + | <td class="ntext">\textrm{c) }</td> |
| + | <td class="ntext" width="100%">6\, framför \,x^2\,, \,2\, framför \,x</td> |
| + | </tr> |
| + | <tr><td height="5px"/></tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning a) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_4a.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning b) </div> |
| + | <div class=NavContent> |
| + | 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 class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning c) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_4c.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | ==Övning 2.1:5== |
| + | <div class="ovning"> |
| + | Förenkla så långt som möjligt |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr align="left"> |
| + | <td class="ntext">a)</td> |
| + | <td class="ntext" width="50%">\displaystyle \frac{1}{x-x^2}-\displaystyle \frac{1}{x}</td> |
| + | <td class="ntext">b)</td> |
| + | <td class="ntext" width="50%">\displaystyle \frac{1}{y^2-2y}-\displaystyle \frac{2}{y^2-4}</td> |
| + | </tr> |
| + | <tr align="left"> |
| + | <td class="ntext">c)</td> |
| + | <td class="ntext" width="50%">\displaystyle \frac{(3x^2-12)(x^2-1)}{(x+1)(x+2)}</td> |
| + | <td class="ntext">d)</td> |
| + | <td class="ntext" width="50%">\displaystyle \frac{(y^2+4y+4)(2y-4)}{(y^2+4)(y^2-4)}</td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Facit </div> |
| + | <div class=NavContent> |
| + | Facit till alla delfrågor |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr align="left"> |
| + | <td class="ntext">a)</td> |
| + | <td class="ntext" width="50%">\displaystyle \frac{1}{1-x}</td> |
| + | <td class="ntext">b)</td> |
| + | <td class="ntext" width="50%">-\displaystyle \frac{1}{y(y+2)}</td> |
| + | </tr> |
| + | <tr align="left"> |
| + | <td class="ntext">c)</td> |
| + | <td class="ntext" width="50%">3(x-2)(x-1)</td> |
| + | <td class="ntext">d)</td> |
| + | <td class="ntext" width="50%">\displaystyle \frac{2(y+2)}{y^2+4}</td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning a) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_5a.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning b) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_5b.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning c) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_5c.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning d) </div> |
| + | <div class=NavContent> |
| + | 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> |
| + | |
| + | ==Övning 2.1:6== |
| + | <div class="ovning"> |
| + | Förenkla så långt som möjligt |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr align="left"> |
| + | <td class="ntext">a)</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" width="50%">\displaystyle \frac{x}{x-2}+\displaystyle \frac{x}{x+3}-2</td> |
| + | </tr> |
| + | <tr align="left"> |
| + | <td class="ntext">c)</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" 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><td height="5px"/></tr> |
| + | </table> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Facit </div> |
| + | <div class=NavContent> |
| + | Facit till alla delfrågor<br \> |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr align="left"> |
| + | <td class="ntext">a)</td> |
| + | <td class="ntext" width="50%">2y</td> |
| + | <td class="ntext">b)</td> |
| + | <td class="ntext" width="50%">\displaystyle\frac{-x+12}{(x-2)(x+3)}</td> |
| + | </tr> |
| + | <tr align="left"> |
| + | <td class="ntext">c)</td> |
| + | <td class="ntext" width="50%">\displaystyle\frac{b}{a(a-b)}</td> |
| + | <td class="ntext">d)</td> |
| + | <td class="ntext" width="50%">\displaystyle\frac{a(a+b)}{4b}</td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning a) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_6a.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning b) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_6b.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning c) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_6c.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning d) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga d) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_6d.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | ==Övning 2.1:7== |
| + | <div class="ovning"> |
| + | Förenkla följande bråkuttryck genom att skriva på gemensamt bråkstreck |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr align="left"> |
| + | <td class="ntext">a)</td> |
| + | <td class="ntext" width="33%">\displaystyle \frac{2}{x+3}-\frac{2}{x+5}</td> |
| + | <td class="ntext">b)</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" width="33%">\displaystyle \frac{ax}{a+1}-\displaystyle \frac{ax^2}{(a+1)^2}</td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Facit </div> |
| + | <div class=NavContent> |
| + | Facit till alla delfrågorna<br \> |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr align="left"> |
| + | <td class="ntext">a)</td> |
| + | <td class="ntext" width="33%">\displaystyle \frac{4}{(x+3)(x+5)}</td> |
| + | <td class="ntext">b)</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" width="33%">\displaystyle \frac{ax(a+1-x)}{(a+1)^2}</td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning a) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_7a.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning b) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_7b.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | <div class=NavFrame style="CLEAR: both"> |
| + | <div class=NavHead>Lösning c) </div> |
| + | <div class=NavContent> |
| + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td align="center"> |
| + | [[Bild:2_1_7c.gif]] |
| + | </td> |
| + | </tr> |
| + | </table> |
| + | </div> |
| + | </div> |
| + | |
| + | ==Övning 2.1:8== |
| + | |
| + | <div class="ovning"> |
| + | Förenkla följande bråkuttryck genom att skriva på gemensamt bråkstreck |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr> |
| + | <td class="ntext">a)</td> |
| + | <td class="ntext" width="33%">\displaystyle \frac{\displaystyle\ \frac{x}{x+1}\ }{\ 3+x\ }</td> |
| + | <td class="ntext">b)</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" width="33%">\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+x}}}</td> |
| + | </tr> |
| + | <tr><td height="5px"/></tr> |
| + | </table> |
| + | </div> |
| + | |
| + | <div class="svar"> |
| + | <table width="100%" cellspacing="10px"> |
| + | <tr align="left"> |
| + | <td class="ntext">a)</td> |
| + | <td class="ntext" width="33%">\displaystyle \frac{x}{(x+3)(x+1)}</td> |
| + | <td class="ntext">b)</td> |
| + | <td class="ntext" width="33%">\displaystyle \frac{2(x-3)}{x}</td> |
| + | <td class="ntext">c)</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> |
| </table> | | </table> |
| </div> | | </div> |