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1. 计算:
(1) $\frac {3ab^{2}}{2x^{3}y}\cdot \frac {8xy}{9a^{2}b}÷\frac {3x}{4b}$； (2) $\frac {2x - 6}{x^{2}-4x + 4}÷\frac {3x - x^{2}}{4x^{2}-16}\cdot \frac {x - 2}{x + 2}$。
(1) $\frac {3ab^{2}}{2x^{3}y}\cdot \frac {8xy}{9a^{2}b}÷\frac {3x}{4b}$； (2) $\frac {2x - 6}{x^{2}-4x + 4}÷\frac {3x - x^{2}}{4x^{2}-16}\cdot \frac {x - 2}{x + 2}$。
答案
解: (1) 原式 $ = \frac{3ab^{2}}{2x^{3}y} \cdot \frac{8xy}{9a^{2}b} \cdot \frac{4b}{3x} $
$ = \frac{16b^{2}}{9ax^{3}} $;
(2) 原式 $ = \frac{2(x - 3)}{(x - 2)^{2}} \cdot \frac{4(x + 2)(x - 2)}{x(3 - x)} \cdot \frac{x - 2}{x + 2} $
$ = -\frac{8}{x} $.
$ = \frac{16b^{2}}{9ax^{3}} $;
(2) 原式 $ = \frac{2(x - 3)}{(x - 2)^{2}} \cdot \frac{4(x + 2)(x - 2)}{x(3 - x)} \cdot \frac{x - 2}{x + 2} $
$ = -\frac{8}{x} $.
2. 计算:
(1) $\frac {3x}{x - 4y}-\frac {x + y}{x - 4y}+\frac {7y}{4y - x}$； (2) $\frac {1}{6xy}+\frac {2}{9x^{2}y}-\frac {5}{3xy^{2}}$；
(3) $\frac {x - 2}{x^{2}-x}+\frac {x + 1}{x - 1}-\frac {2}{x}$； (4) $\frac {2}{a - 1}-a + 2$；
(1) $\frac {3x}{x - 4y}-\frac {x + y}{x - 4y}+\frac {7y}{4y - x}$； (2) $\frac {1}{6xy}+\frac {2}{9x^{2}y}-\frac {5}{3xy^{2}}$；
(3) $\frac {x - 2}{x^{2}-x}+\frac {x + 1}{x - 1}-\frac {2}{x}$； (4) $\frac {2}{a - 1}-a + 2$；
答案
解: (1) 原式 $ = \frac{3x - (x + y) - 7y}{x - 4y} $
$ = \frac{2x - 8y}{x - 4y} $
$ = \frac{2(x - 4y)}{x - 4y} $
$ = 2 $;
(2) 原式 $ = \frac{3xy}{18x^{2}y^{2}} + \frac{4y}{18x^{2}y^{2}} - \frac{30x}{18x^{2}y^{2}} $
$ = \frac{3xy + 4y - 30x}{18x^{2}y^{2}} $;
(3) 原式 $ = \frac{x - 2 + x(x + 1) - 2(x - 1)}{x(x - 1)} $
$ = \frac{x^{2}}{x(x - 1)} = \frac{x}{x - 1} $;
(4) 原式 $ = \frac{2}{a - 1} - \frac{(a - 2)(a - 1)}{a - 1} $
$ = \frac{2 - (a^{2} - 3a + 2)}{a - 1} $
$ = \frac{3a - a^{2}}{a - 1} $.
$ = \frac{2x - 8y}{x - 4y} $
$ = \frac{2(x - 4y)}{x - 4y} $
$ = 2 $;
(2) 原式 $ = \frac{3xy}{18x^{2}y^{2}} + \frac{4y}{18x^{2}y^{2}} - \frac{30x}{18x^{2}y^{2}} $
$ = \frac{3xy + 4y - 30x}{18x^{2}y^{2}} $;
(3) 原式 $ = \frac{x - 2 + x(x + 1) - 2(x - 1)}{x(x - 1)} $
$ = \frac{x^{2}}{x(x - 1)} = \frac{x}{x - 1} $;
(4) 原式 $ = \frac{2}{a - 1} - \frac{(a - 2)(a - 1)}{a - 1} $
$ = \frac{2 - (a^{2} - 3a + 2)}{a - 1} $
$ = \frac{3a - a^{2}}{a - 1} $.
3. 计算:
(1) $(\frac {3x}{y^{2}})^{3}\cdot \frac {y^{3}}{4x^{2}}-\frac {2}{x^{2}}÷(\frac {y}{x})^{3}$； (2) $\frac {a^{2}-9}{a + 2}÷(a + 4+\frac {1}{a + 2})$；
(3) $(\frac {m}{m - 2n}-\frac {3n}{m - 2n})\cdot \frac {mn}{m - 3n}+\frac {2mn^{2}}{(m - 2n)^{2}}$； (4) $(\frac {a + b}{a - b})^{2}\cdot \frac {a - b}{a + b}-\frac {a^{2}}{a^{2}-b^{2}}÷\frac {a}{4b}$。
(1) $(\frac {3x}{y^{2}})^{3}\cdot \frac {y^{3}}{4x^{2}}-\frac {2}{x^{2}}÷(\frac {y}{x})^{3}$； (2) $\frac {a^{2}-9}{a + 2}÷(a + 4+\frac {1}{a + 2})$；
(3) $(\frac {m}{m - 2n}-\frac {3n}{m - 2n})\cdot \frac {mn}{m - 3n}+\frac {2mn^{2}}{(m - 2n)^{2}}$； (4) $(\frac {a + b}{a - b})^{2}\cdot \frac {a - b}{a + b}-\frac {a^{2}}{a^{2}-b^{2}}÷\frac {a}{4b}$。
答案
解: (1) 原式 $ = \frac{27x^{3}}{y^{6}} \cdot \frac{y^{3}}{4x^{2}} - \frac{2}{x^{2}} \cdot \frac{x^{3}}{y^{3}} $
$ = \frac{27x}{4y^{3}} - \frac{2x}{y^{3}} $
$ = \frac{19x}{4y^{3}} $;
(2) 原式 $ = \frac{(a + 3)(a - 3)}{a + 2} \div \frac{(a + 4)(a + 2) + 1}{a + 2} $
$ = \frac{(a + 3)(a - 3)}{a + 2} \cdot \frac{a + 2}{(a + 3)^{2}} $
$ = \frac{a - 3}{a + 3} $;
(3) 原式 $ = \frac{m - 3n}{m - 2n} \cdot \frac{mn}{m - 3n} + \frac{2mn^{2}}{(m - 2n)^{2}} $
$ = \frac{mn}{m - 2n} + \frac{2mn^{2}}{(m - 2n)^{2}} $
$ = \frac{mn(m - 2n) + 2mn^{2}}{(m - 2n)^{2}} $
$ = \frac{m^{2}n}{(m - 2n)^{2}} $;
(4) 原式 $ = \frac{(a + b)^{2}}{(a - b)^{2}} \cdot \frac{a - b}{a + b} - \frac{a^{2}}{(a + b)(a - b)} \cdot \frac{4b}{a} $
$ = \frac{a + b}{a - b} - \frac{4ab}{(a + b)(a - b)} $
$ = \frac{(a + b)^{2} - 4ab}{(a + b)(a - b)} $
$ = \frac{(a - b)^{2}}{(a + b)(a - b)} $
$ = \frac{a - b}{a + b} $.
$ = \frac{27x}{4y^{3}} - \frac{2x}{y^{3}} $
$ = \frac{19x}{4y^{3}} $;
(2) 原式 $ = \frac{(a + 3)(a - 3)}{a + 2} \div \frac{(a + 4)(a + 2) + 1}{a + 2} $
$ = \frac{(a + 3)(a - 3)}{a + 2} \cdot \frac{a + 2}{(a + 3)^{2}} $
$ = \frac{a - 3}{a + 3} $;
(3) 原式 $ = \frac{m - 3n}{m - 2n} \cdot \frac{mn}{m - 3n} + \frac{2mn^{2}}{(m - 2n)^{2}} $
$ = \frac{mn}{m - 2n} + \frac{2mn^{2}}{(m - 2n)^{2}} $
$ = \frac{mn(m - 2n) + 2mn^{2}}{(m - 2n)^{2}} $
$ = \frac{m^{2}n}{(m - 2n)^{2}} $;
(4) 原式 $ = \frac{(a + b)^{2}}{(a - b)^{2}} \cdot \frac{a - b}{a + b} - \frac{a^{2}}{(a + b)(a - b)} \cdot \frac{4b}{a} $
$ = \frac{a + b}{a - b} - \frac{4ab}{(a + b)(a - b)} $
$ = \frac{(a + b)^{2} - 4ab}{(a + b)(a - b)} $
$ = \frac{(a - b)^{2}}{(a + b)(a - b)} $
$ = \frac{a - b}{a + b} $.
