第150页 - 经纶学典学霸八年级数学上下册【江苏国标】

$ \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}$

$解:原式=\frac{2x-2-x}{x(x-1)}+\ \frac{(x-2)^{2} }{x(x-2)}$

$~~~~~~~~~~~~~~~~=\frac{x-2}{x(x-1)}+\frac{x-2}{x}=\frac{x-2}{x(x-1)}+\frac{x²-3x+2}{x(x-1)}$

$~~~~~~~~~~~~~~~~=\frac{x²-2x}{x(x-1)} =\frac{x(x-2)}{x(x-1)}= \frac{x-2}{x-1}.$

$解:原式=\frac {x²}{(x+1)² }÷\frac {x²+x-x}{x+1}$

$~~~~~~~~~~~~~~~~=\frac{x²}{(x+1)²}÷\frac{x²}{x+1}$

$~~~~~~~~~~~~~~~~=\frac{x²}{(x+1)²}·\frac {x+1}{x²}=\frac{1}{x+1}.$

（更多请点击查看作业精灵详解）

解:去分母，得(x+1)(x-1)-5=(x+1)(x-2)，

去括号，得x²-1-5=x²-x-2，解得x=4.

检验:当x=4时，(x+1)(x-2)≠0，

故方程的解为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 {b}{a}} \\ &=-\frac{3}{2} \sqrt{ab^{5} ·a^{3} b·\frac{a}{b}} \\ &= -\frac{3}{2} \sqrt{a^{5} b^{5} ·} \\ &=-\frac {3}{2}a²b²\sqrt {ab} . \\ \end{aligned}$