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電子課本網(wǎng) 第150頁

第150頁

信息發(fā)布者:
$ \begin{aligned} 解:原式&=\frac{a}{a-1}-\frac {1}{a-1} \\ &=\frac{a-1}{a-1} \\ &=1. \\ \end{aligned}$
$ \begin{aligned}解:原式&= \frac{a2-1}{a}·\frac{a}{(a-1)2} \\ &= \frac{(a+1)(a-1)}{a}·\frac{a}{(a-1)2} \\ &= \frac{a+1}{a-1}. \\ \end{aligned}$
$解:原式=\frac{2x-2-x}{x(x-1)}+\ \frac{(x-2)^{2} }{x(x-2)}$
$~~~~~~~~~~~~~~~~=\frac{x-2}{x(x-1)}+\frac{x-2}{x}=\frac{x-2}{x(x-1)}+\frac{x2-3x+2}{x(x-1)}$
$~~~~~~~~~~~~~~~~=\frac{x2-2x}{x(x-1)} =\frac{x(x-2)}{x(x-1)}= \frac{x-2}{x-1}.$
$解:原式=\frac {x2}{(x+1)2 }÷\frac {x2+x-x}{x+1}$
$~~~~~~~~~~~~~~~~=\frac{x2}{(x+1)2}÷\frac{x2}{x+1}$
$~~~~~~~~~~~~~~~~=\frac{x2}{(x+1)2}·\frac {x+1}{x2}=\frac{1}{x+1}.$
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解:去分母,得(x+1)(x-1)-5=(x+1)(x-2),
去括號,得x2-1-5=x2-x-2,解得x=4.
檢驗:當x=4時,(x+1)(x-2)≠0,
故方程的解為x=4.
$ \begin{aligned}解:原式&=3\sqrt{6}-(5-\sqrt{6})+18 \\ &=3\sqrt {6} -5+\sqrt{6}+18 \\ &=4\sqrt {6} +13. \\ \end{aligned}$
$ \begin{aligned}解:原式&=\frac{\sqrt {5} }{\sqrt {3} }× \sqrt{15}-\frac{\sqrt{5}}{\sqrt {3} }×2\sqrt {3} \\ &=5-2\sqrt {5} . \\ \end{aligned}$
$ \begin{aligned} 解:原式&= \sqrt{48}÷ \sqrt{27}+ \frac {\sqrt {6} }{4}÷\sqrt {27} \\ &= \sqrt{\frac{16}{9}}+\frac {1}{4}\sqrt {\frac {2}{9}}=\frac{4}{3}+\frac {\sqrt {2} }{12}. \\ \end{aligned}$
$ \begin{aligned} 解:原式&=-\frac{3}{2} \sqrt{ab^{5} ·a^{3}b÷\frac {a}} \\ &=-\frac{3}{2} \sqrt{ab^{5} ·a^{3} b·\frac{a}} \\ &= -\frac{3}{2} \sqrt{a^{5} b^{5} ·} \\ &=-\frac {3}{2}a2b2\sqrt {ab} . \\ \end{aligned}$
$ \begin{aligned}解:原式&=\frac {a2-4}{a2} ÷\frac{a-2}{a} \\ &=\frac{(a+2)(a-2)}{a2}·\frac{a}{a-2} \\ &=\frac{a+2}{a}, \\ \end{aligned}$
$當a=5時,$
$ \begin{aligned}原式&= \frac{5+2}{5} \\ &= \frac{7}{5}. \\ \end{aligned}$
$ \begin{aligned}解:原式&=\frac{(x-1)(x+1)-x(x-2)}{x(x+1)}· \frac{(x+1)2}{x(2x-1)} \\ &=\frac{2x-1}{x(x+1)}· \frac{(x+1)2}{x(2x-1)} \\ &=\frac{x+1}{x2}. \\ ∵x2-x-1&=0, \\ ∴x2&=x+1, \\ \end{aligned}$
$∴\frac{x+1}{x2}=\frac{x+1}{x+1}=1.$
$ \begin{aligned}解:原式&=\frac{(a-3)2}{a-2}÷[\frac {(2+a)(2-a)}{2-a}+\frac {5}{2-a} ] \\ &=\frac{(a-3)2}{a-2}÷\frac{4-a2+5}{2-a} \\ &= \frac{(a-3)2}{a-2}· \frac{2-a}{(3+a)(3-a)}\ \\ &=\frac{a-3}{a+3}, \\ \end{aligned}$
$解不等式\frac{a-1}{2}≤1得a≤3,$
$∵a為正整數(shù),$
$∴a=1,2,3.$
$∵要使分式有意義,則a-2≠0,$
$∴a=2.$
$∵當a=3時,$
$a+2+\frac {5}{2-a}=3+2+\frac{5}{2-3}=0,$
$∴a≠3,$
$∴a=1.$
$把a=1代入得原式=\frac{1-3}{1+3}=-\frac{1}{2}.$
$解:去分母,得1+2(x-2)=-(1-x),$
$去括號,得1+2x-4=-1+x,\ $
$移項,得2x-x=-1-1+4,$
$解得x=2.$
$檢驗:當x=2時,x-2=0,$
$∴x=2是原方程的增根,$
$∴原方程無解.$
$解:去分母,得3(x-1)+6x-(x+5)=0,$
$去括號,得3x-3+6x-x-5=0,\ $
$移項,得3x+6x-x=3+5,$
$合并同類項,得8x=8,解得x=1.$
$檢驗:把x=1代入x(x-1),得x(x-1)=0,$
$∴x=1是原方程的增根,$
$∴原方程無解.$