有理式测验：化简、求解与取值限制

Question 1

化简并写出所有需排除的取值：$$\frac{x^2-9}{x-3}$$

Accepted Answer

$x+3$，且 $x
eq 3$

Answer

$x+3$，无需要排除的取值

Answer

$\frac{x^2-9}{x-3}$，已经最简

Answer

$x-3$，且 $x
eq 3$

Question 2

计算并化简：$$\frac{2x}{x-3}\div\frac{4}{x+1}$$

Accepted Answer

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

Answer

$\frac{8x}{(x-3)(x+1)}$

Answer

$\frac{2x}{x-3}\cdot\frac{4}{x+1}=\frac{8x}{(x-3)(x+1)}$

Answer

$\frac{2x(x+1)}{4(x-3)}$（不能约分）

Question 3

求解并写出取值限制：$$\frac{x+2}{x-1}=\frac{x-1}{x+2}$$

Accepted Answer

$x=-	frac{1}{2}$，且 $x
eq 1,-2$

Answer

$x=1$

Answer

$x=0$，且 $x
eq 1,-2$

Answer

$x=-2$

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