1. 计算：$x\div(\frac{1}{x}-\frac{1}{y})=$_______.

$\frac{x^{2}y}{y - x}$

2. $a\div\frac{a}{b}\cdot\frac{1}{a}=(\ \ \ \ )$.
A. 1
B. $ab$
C. $\frac{b}{a}$
D. $\frac{a}{b}$

C

3. 计算：
(1) $(1+\frac{1}{x - 1})\div\frac{x}{x^{2}-1}$； (2) $(xy - x^{2})(\frac{1}{x}-\frac{1}{y - x})$；
(3) $\frac{x^{2}+xy}{x^{2}-xy}\div(x + y)\div\frac{-xy}{y^{2}-xy}$； (4) $\frac{a^{2}-16}{(a - 2)(a + 4)}\div(a - 2)\cdot\frac{a^{2}+4 - 4a}{a - 2}$.

(1) $x + 1$; (2) $y - 2x$; (3) $\frac{1}{x}$; (4) $\frac{a - 4}{a - 2}$

4. 化简、求值：$\frac{1}{x + 2}-\frac{x^{2}+2x + 1}{x + 2}\div\frac{x^{2}-1}{x - 1}$，其中$x = 2$.

$-\frac{1}{2}$