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# 有理表达式的加减介绍

## 有理式的加减法 （在分母相同的情况下）

### 数字分数

$\begin{array}{rl}& \phantom{=}\frac{4}{5}-\frac{1}{5}\\ \\ & =\frac{4-1}{5}\\ \\ & =\frac{3}{5}\end{array}$

### 变量表达式

$\begin{array}{rl}& \phantom{=}\frac{7a+3}{a+2}+\frac{2a-1}{a+2}\\ \\ & =\frac{\left(7a+3\right)+\left(2a-1\right)}{a+2}\\ \\ & =\frac{7a+3+2a-1}{a+2}\\ \\ & =\frac{9a+2}{a+2}\end{array}$

$\begin{array}{rl}& \phantom{=}\frac{b+1}{{b}^{2}}-\frac{4-b}{{b}^{2}}\\ \\ & =\frac{\left(b+1\right)-\left(4-b\right)}{{b}^{2}}\\ \\ & =\frac{b+1-4+b}{{b}^{2}}\\ \\ & =\frac{2b-3}{{b}^{2}}\end{array}$

### 看看你的知识掌握地如何

$\frac{x+5}{x-1}+\frac{2x-3}{x-1}=$

$\frac{x+1}{2x}-\frac{5x-2}{2x}=$

## 有理式的加减法（在分母不同的情况下）

### 数字分数

$\begin{array}{rl}& \phantom{=}\frac{2}{3}+\frac{1}{2}\\ \\ & =\frac{2}{3}\left(\frac{2}{2}\right)+\frac{1}{2}\left(\frac{3}{3}\right)\\ \\ & =\frac{4}{6}+\frac{3}{6}\\ \\ & =\frac{7}{6}\end{array}$

• 第一个分数中的分母 ($3$) 需要乘以 $2$
• 第二个分数中的分母 ($2$) 则需要乘以 $3$

### 变量表达式

$\frac{1}{x-3}+\frac{2}{x+5}$

$\begin{array}{rl}& \phantom{=}\frac{1}{x-3}+\frac{2}{x+5}\\ \\ & =\frac{1}{x-3}\left(\frac{x+5}{x+5}\right)+\frac{2}{x+5}\left(\frac{x-3}{x-3}\right)\\ \\ & =\frac{1\left(x+5\right)}{\left(x-3\right)\left(x+5\right)}+\frac{2\left(x-3\right)}{\left(x+5\right)\left(x-3\right)}\\ \\ & =\frac{1\left(x+5\right)+2\left(x-3\right)}{\left(x-3\right)\left(x+5\right)}\\ \\ & =\frac{1x+5+2x-6}{\left(x-3\right)\left(x+5\right)}\\ \\ & =\frac{3x-1}{\left(x-3\right)\left(x+5\right)}\end{array}$

### 看看你的知识掌握地如何

$\frac{3}{x+4}+\frac{2}{x-2}=$

$\frac{2}{x-1}-\frac{5}{x}=$