If you're seeing this message, it means we're having trouble loading external resources on our website.

# 简化有理表达式 (高级)

## 例题 1: 简化 ‍

$\frac{10{x}^{3}}{2{x}^{2}-18x}=\frac{2\cdot 5\cdot x\cdot {x}^{2}}{2\cdot x\cdot \left(x-9\right)}$

$\begin{array}{rl}\frac{2\cdot 5\cdot x\cdot {x}^{2}}{2\cdot x\cdot \left(x-9\right)}& =\frac{\overline{)2}\cdot 5\cdot \overline{)x}\cdot {x}^{2}}{\overline{)2}\cdot \overline{)x}\cdot \left(x-9\right)}\\ \\ & =\frac{5{x}^{2}}{x-9}\end{array}$

$\frac{5{x}^{2}}{x-9}$ 并且 $x\ne 0$

### 看看你对知识掌握得如何

1) 简化 $\frac{6{x}^{2}}{12{x}^{4}-9{x}^{3}}$.

## 例题 2: 简化‍

$\begin{array}{rl}& \phantom{=}\frac{\left(3-x\right)\left(x-1\right)}{\left(x-3\right)\left(x+1\right)}\\ \\ & =\frac{-1\left(-3+x\right)\left(x-1\right)}{\left(x-3\right)\left(x+1\right)}\\ \\ & =\frac{-1\left(x-3\right)\left(x-1\right)}{\left(x-3\right)\left(x+1\right)}\phantom{\rule{1em}{0ex}}\text{交换律}\end{array}$

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

$\frac{1-x}{x+1}$ 并且 $x\ne 3$

### 看看你的知识掌握地如何

2) 化简 $\frac{\left(x-2\right)\left(x-5\right)}{\left(2-x\right)\left(x+5\right)}$.

3) 化简 $\frac{15-10x}{8{x}^{3}-12{x}^{2}}$.

## 让我们再多做一些练习。

4) 简化 $\frac{3x}{15{x}^{2}-6x}$.

5) 化简 $\frac{3{x}^{3}-15{x}^{2}+12x}{3x-3}$.

6) 化简 $\frac{6{x}^{2}-12x}{6x-3{x}^{2}}$.