第44页

信息发布者：
乘方
乘除
加减
括号里面的
从左往右
A
D
$m$
$-\frac{1}{a + 1}$
解：
$\begin{aligned}&\frac{2a}{a + 1}-\frac{2a - 4}{a^{2}-1}\div\frac{a - 2}{a^{2}-2a + 1}\\=&\frac{2a}{a + 1}-\frac{2(a - 2)}{(a + 1)(a - 1)}\cdot\frac{(a - 1)^{2}}{a - 2}\\=&\frac{2a}{a + 1}-\frac{2(a - 1)}{a + 1}\\=&\frac{2a-2(a - 1)}{a + 1}\\=&\frac{2a-2a + 2}{a + 1}\\=&\frac{2}{a + 1}\end{aligned}$
解：
$\begin{aligned}&(\frac{2x}{x^{2}-1}-\frac{1}{x - 1})\div\frac{x}{x + 1}\\=&[\frac{2x}{(x + 1)(x - 1)}-\frac{x + 1}{(x + 1)(x - 1)}]\div\frac{x}{x + 1}\\=&\frac{2x-(x + 1)}{(x + 1)(x - 1)}\cdot\frac{x + 1}{x}\\=&\frac{2x-x - 1}{(x + 1)(x - 1)}\cdot\frac{x + 1}{x}\\=&\frac{x - 1}{(x + 1)(x - 1)}\cdot\frac{x + 1}{x}\\=&\frac{1}{x}\end{aligned}$
解：
$\begin{aligned}&\frac{a^{2}-3a}{a^{2}+a}\div\frac{a - 3}{a^{2}-1}\cdot\frac{a + 1}{a - 1}\\=&\frac{a(a - 3)}{a(a + 1)}\cdot\frac{(a + 1)(a - 1)}{a - 3}\cdot\frac{a + 1}{a - 1}\\=&(a - 1)\cdot\frac{a + 1}{a - 1}\\=&a + 1\end{aligned}$
解：
$\begin{aligned}&m - 1+\frac{2m - 6}{m^{2}-9}\div\frac{2m + 2}{m + 3}\\=&m - 1+\frac{2(m - 3)}{(m + 3)(m - 3)}\cdot\frac{m + 3}{2(m + 1)}\\=&m - 1+\frac{1}{m + 1}\\=&\frac{(m - 1)(m + 1)+1}{m + 1}\\=&\frac{m^{2}-1 + 1}{m + 1}\\=&\frac{m^{2}}{m + 1}\end{aligned}$
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