6. 计算:(1)$9a^{2}\cdot\frac{b^{2}}{3a}=$；(2)$\frac{1}{x}÷ x=$.

(1)$3ab^{2}$；(2)$\frac{1}{x^{2}}$

(1) $9a^{2}\cdot\frac{b^{2}}{3a} = (9÷3)\cdot(a^{2}÷ a)\cdot b^{2} = 3ab^{2}$；
(2) $\frac{1}{x}÷ x = \frac{1}{x}\cdot\frac{1}{x} = \frac{1}{x^{2}}$

7. 计算:$\frac{m^{2}+mn}{m-n}÷\frac{mn}{m-n}= $.

$\frac{m+n}{n}$对应的选项

$\frac{m^{2}+mn}{m-n}÷\frac{mn}{m-n}$
$=\frac{m(m+n)}{m-n}×\frac{m-n}{mn}$
$=\frac{m+n}{n}$

8. 已知$\frac{3-2x}{x-1}÷ A= \frac{1}{x-1}$,则代数式$A= $.

$3-2x$（或写作$-(2x-3)$的简化形式，但在此选择最简形式$3-2x$）

$A=\frac{3-2x}{x-1}÷\frac{1}{x-1}=\frac{3-2x}{x-1}\cdot(x-1)=3-2x$
$3-2x$

9. 计算:$(xy-x^{2})\cdot\frac{xy}{x-y}=$.

-x²y

$(xy - x^2) \cdot \frac{xy}{x - y} = x(y - x) \cdot \frac{xy}{x - y} = -x(x - y) \cdot \frac{xy}{x - y} = -x^2y$

10. 如果$x-3y= 0$,那么代数式$\frac{2x+y}{x^{2}-2xy+y^{2}}\cdot(x-y)$的值为.

$\frac{7}{2}$

由$x - 3y = 0$，得$x = 3y$。
$\begin{aligned}&\frac{2x + y}{x^2 - 2xy + y^2} \cdot (x - y)\\=&\frac{2x + y}{(x - y)^2} \cdot (x - y)\\=&\frac{2x + y}{x - y}\end{aligned}$
将$x = 3y$代入上式：
$\begin{aligned}\frac{2 \cdot 3y + y}{3y - y}&=\frac{6y + y}{2y}\\&=\frac{7y}{2y}\\&=\frac{7}{2}\end{aligned}$
$\frac{7}{2}$

11. 计算:
(1)$(-16x^{4}y)÷(-\frac{4x^{2}}{y})$；
(2)$\frac{x^{2}-4x+4}{x^{2}-2x}÷\frac{x^{2}-4}{2x}$；
(3)$\frac{m+3}{1-m}÷\frac{m^{2}+3m}{m^{2}-2m+1}$.

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

(1)
$\begin{aligned}(-16x^{4}y)÷(-\frac{4x^{2}}{y})&=(-16x^{4}y)×(-\frac{y}{4x^{2}})\\&=(-16)×(-\frac{1}{4})× x^{4-2}× y× y\\&=4x^{2}y^{2}\end{aligned}$
(2)
$\begin{aligned}\frac{x^{2}-4x+4}{x^{2}-2x}÷\frac{x^{2}-4}{2x}&=\frac{(x-2)^{2}}{x(x-2)}×\frac{2x}{(x+2)(x-2)}\\&=\frac{x-2}{x}×\frac{2x}{(x+2)(x-2)}\\&=\frac{2}{x+2}\end{aligned}$
(3)
$\begin{aligned}\frac{m+3}{1-m}÷\frac{m^{2}+3m}{m^{2}-2m+1}&=\frac{m+3}{-(m-1)}×\frac{(m-1)^{2}}{m(m+3)}\\&=-\frac{(m+3)(m-1)^{2}}{m(m-1)(m+3)}\\&=-\frac{m-1}{m}\\&=\frac{1-m}{m}\end{aligned}$