【典型例题 1】计算：
(1)$8x^{2}y^{4}\cdot (-\frac {3x}{4y^{3}})÷(-\frac {x^{2}y}{2})$；
(2)$-\frac {x-y}{x+2y}÷\frac {x^{2}-y^{2}}{x^{2}+4xy+4y^{2}}\cdot \frac {x-y}{x+2y}$。

思路导引 分式的乘除混合运算,可以按照从左到右的顺序进行,也可以统一成乘法运算。
【解】
(1)$8x^{2}y^{4}\cdot (-\frac {3x}{4y^{3}})÷(-\frac {x^{2}y}{2}) = (8x^{2}y^{4})\cdot (-\frac {3x}{4y^{3}})\cdot (-\frac {2}{x^{2}y}) = 12x$。
(2)$-\frac {x-y}{x+2y}÷\frac {x^{2}-y^{2}}{x^{2}+4xy+4y^{2}}\cdot \frac {x-y}{x+2y} = -\frac {x-y}{x+2y}\cdot \frac {(x+2y)^{2}}{(x+y)(x-y)}\cdot \frac {x-y}{x+2y} = -\frac {x-y}{x+y}$。

1. 计算：$\frac {m}{3m+9}\cdot \frac {6}{9-m^{2}}÷\frac {2m}{m-3} = $()
A.$\frac {1}{(m+3)^{2}}$
B.$-\frac {1}{(m+3)^{2}}$
C.$\frac {1}{(m-3)^{2}}$
D.$-\frac {1}{m^{2}+9}$

B

原式=$\frac{m}{3(m + 3)} \cdot \frac{6}{-(m - 3)(m + 3)} \cdot \frac{m - 3}{2m}$
=$\frac{m \cdot 6 \cdot (m - 3)}{3(m + 3) \cdot [-(m - 3)(m + 3)] \cdot 2m}$
约分（数字：6与3×2约；字母：m与m约，(m - 3)与(m - 3)约）后得$-\frac{1}{(m + 3)^2}$

2. 计算$\frac {a^{2}x}{b^{2}y}÷\frac {bx}{ay}\cdot \frac {by}{ax}$的结果为。

【解析】：原式$=\frac{a^{2}x}{b^{2}y}\cdot \frac{ay}{bx}\cdot \frac{by}{ax}=\frac{a^{2}x\cdot ay\cdot by}{b^{2}y\cdot bx\cdot ax}=\frac{a^{3}bxy^{2}}{ab^{3}x^{2}y}=\frac{a^{2}}{b^{2}x}$
【答案】：$\frac{a^{2}}{b^{2}x}$

【典型例题 2】计算：
(1)$(\frac {-nc^{3}}{3m})^{2}$；
(2)$(\frac {c}{ab})^{2}\cdot (-\frac {b}{ac})^{3}÷(-\frac {b}{a})^{4}$。

【解】(1)$(\frac {-nc^{3}}{3m})^{2} = \frac {(-nc^{3})^{2}}{(3m)^{2}} = \frac {n^{2}c^{6}}{9m^{2}}$。
(2)$(\frac {c}{ab})^{2}\cdot (-\frac {b}{ac})^{3}÷(-\frac {b}{a})^{4} = -\frac {c^{2}}{a^{2}b^{2}}\cdot \frac {b^{3}}{a^{3}c^{3}}\cdot \frac {a^{4}}{b^{4}} = -\frac {1}{ab^{3}c}$。

3. 计算：
(1)$(-\frac {n}{m})^{3}\cdot (-\frac {m}{n})^{2}$；
(2)$(\frac {2x}{3y})^{2}\cdot (-\frac {3y}{4x})^{3}÷(\frac {1}{4}xy)$。

(1) $(-\frac{n}{m})^{3}\cdot(-\frac{m}{n})^{2}$
$=-\frac{n^{3}}{m^{3}}\cdot\frac{m^{2}}{n^{2}}$
$=-\frac{n^{3}m^{2}}{m^{3}n^{2}}$
$=-\frac{n}{m}$
(2) $(\frac{2x}{3y})^{2}\cdot(-\frac{3y}{4x})^{3}÷(\frac{1}{4}xy)$
$=\frac{4x^{2}}{9y^{2}}\cdot(-\frac{27y^{3}}{64x^{3}})\cdot4xy$
$=\frac{4x^{2}\cdot(-27y^{3})\cdot4xy}{9y^{2}\cdot64x^{3}}$
$=\frac{-432x^{3}y^{4}}{576x^{3}y^{2}}$
$=-\frac{3y^{2}}{4}$