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Övningar 2.1 - Versionshistorik
2026-05-16T17:26:48Z
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KTH.SE:u1zpa8nw den 17 juli 2007 kl. 09.38
2007-07-17T09:38:12Z
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KTH.SE:u1zpa8nw den 16 juli 2007 kl. 10.44
2007-07-16T10:44:46Z
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KTH.SE:u1zpa8nw: Ny sida: __NOTOC__ ==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> <t...
2007-07-16T08:00:35Z
<p>Ny sida: __NOTOC__ ==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> <t...</p>
<p><b>Ny sida</b></p><div>__NOTOC__<br />
==Övning 2.1:1==<br />
<div class="ovning"><br />
Utveckla<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$3x(x-1)$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$(1+x-x^2)xy$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$-x^2(4-y^2)$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="33%">$x^3y^2\left(\displaystyle \frac{1}{y} - \frac{1}{xy}+1\right)$</td><br />
<td class="ntext">e) </td><br />
<td class="ntext" width="33%">$(x-7)^2$</td><br />
<td class="ntext">f)</td><br />
<td class="ntext" width="33%">$(5+4y)^2$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">g)</td><br />
<td class="ntext" width="33%">$(y^2-3x^3)^2$</td><br />
<td class="ntext">h)</td><br />
<td class="ntext" width="33%">$(5x^3+3x^5)^2$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 2.1:2==<br />
<div class="ovning"><br />
Utveckla och förenkla så långt som möjligt<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$(x-4)(x-5)-3x(2x-3)$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$(1-5x)(1+15x)-3(2-5x)(2+5x)$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$(3x+4)^2-(3x-2)(3x-8)$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">$(3x^2+2)(3x^2-2)(9x^4+4)$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="50%">$(a+b)^2+(a-b)^2$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 2.1:3==<br />
<br />
<div class="ovning"><br />
Faktorisera s&aring; l&aring;ngt som m&ouml;jligt<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$x^2-36$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$5x^2-20$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$x^2+6x+9$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="33%">$x^2-10x+25$</td><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="33%">$18x-2x^3$</td><br />
<td class="ntext">f)</td><br />
<td class="ntext" width="33%">$16x^2+8x+1$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 2.1:4==<br />
<div class="ovning"><br />
Bestäm koefficienterna framför $\,x\,$ och $\,x^2\,$ när följande uttryck utvecklas<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="100%">$(x+2)(3x^2-x+5)$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="100%">$(1+x+x^2+x^3)(2-x+x^2+x^4)$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="100%">$(x-x^3+x^5)(1+3x+5x^2)(2-7x^2-x^4)$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 2.1:5==<br />
<div class="ovning"><br />
Förenkla så långt som möjligt<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$\displaystyle \frac{1}{x-x^2}-\displaystyle \frac{1}{x}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$\displaystyle \frac{1}{y^2-2y}-\displaystyle \frac{2}{y^2-4}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$\displaystyle \frac{(3x^2-12)(x^2-1)}{(x+1)(x+2)}$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">$\displaystyle \frac{(y^2+4y+4)(2y-4)}{(y^2+4)(y^2-4)}$</td><br />
</tr><br />
</table><br />
</div><br />
<br />
==Övning 2.1:6==<br />
<div class="ovning"><br />
Förenkla så långt som möjligt<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$\left(x-y+\displaystyle\frac{x^2}{y-x}\right)$ $\left(\displaystyle\frac{y}{2x-y}-1\right)$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$\displaystyle \frac{x}{x-2}+\displaystyle \frac{x}{x+3}-2$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$\displaystyle \frac{2a+b}{a^2-ab}-\frac{2}{a-b}$</td><br />
<td class="ntext">d)</td><br />
<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><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==Övning 2.1:7==<br />
<div class="ovning"><br />
Förenkla följande bråkuttryck genom att skriva på gemensamt bråkstreck<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{2}{x+3}-\frac{2}{x+5}$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$x+\displaystyle \frac{1}{x-1}+\displaystyle \frac{1}{x^2}$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{ax}{a+1}-\displaystyle \frac{ax^2}{(a+1)^2}$</td><br />
</tr><br />
</table><br />
</div><br />
<br />
==Övning 2.1:8==<br />
<br />
<div class="ovning"><br />
Förenkla följande bråkuttryck genom att skriva på gemensamt bråkstreck<br />
<table width="100%" cellspacing="10px"><br />
<tr><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{\displaystyle\ \frac{x}{x+1}\ }{\ 3+x\ }$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{\displaystyle \frac{3}{x}-\displaystyle \frac{1}{x}}{\displaystyle \frac{1}{x-3}}$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+x}}}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div></div>
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