1. 通分：
(1) $\frac{1}{ax},\frac{1}{bx}$；
(2) $\frac{3}{2x^{2}y},\frac{5}{3xy^{2}}$；
(3) $\frac{x - 1}{2x^{2}},\frac{2}{3ax}$；
(4) $\frac{a}{2b},\frac{b}{3a},\frac{c}{4ab}$；
(5) $\frac{4a}{5b^{2}c},\frac{3c}{10a^{2}b},-\frac{5b}{-2ac^{2}}$；
(6) $\frac{3a}{2a - b},-\frac{1}{b - 2a}$。
答案：1. 解: (1) $\frac{1}{ax} = \frac{b}{abx}, \frac{1}{bx} = \frac{a}{abx}$.
(2) $\frac{3}{2x^{2}y} = \frac{9y}{6x^{2}y^{2}}, \frac{5}{3xy^{2}} = \frac{10x}{6x^{2}y^{2}}$.
(3) $\frac{x - 1}{2x^{2}} = \frac{3a(x - 1)}{6ax^{2}}, \frac{2}{3ax} = \frac{4x}{6ax^{2}}$.
(4) $\frac{a}{2b} = \frac{6a^{2}}{12ab}, \frac{b}{3a} = \frac{4b^{2}}{12ab}, \frac{c}{4ab} = \frac{3c}{12ab}$.
(5) $\frac{4a}{5b^{2}c} = \frac{8a^{3}c}{10a^{2}b^{2}c^{2}}, \frac{3c}{10a^{2}b} = \frac{3bc^{3}}{10a^{2}b^{2}c^{2}}, \frac{5b}{-2ac^{2}} = -\frac{25ab^{3}}{10a^{2}b^{2}c^{2}}$.
(6) $\frac{3a}{2a - b}, -\frac{1}{b - 2a} = \frac{1}{2a - b}$.
2. 通分：
(1) $\frac{3}{x + 1},\frac{2}{x + 2}$；
(2) $\frac{b}{a - x},\frac{c}{ay - xy}$；
(3) $\frac{x + 1}{x^{2} - x},\frac{x - 1}{x^{2} + x}$；
(4) $\frac{2}{9 - 3a},\frac{a - 1}{a^{2} - 9}$；
(5) $\frac{2a}{a^{2} - 9},\frac{3}{a^{2} - 6a + 9}$；
(6) $\frac{1}{x + 1},\frac{x - 1}{x^{2} + 2x + 1},\frac{1}{x - 1}$；
(7) $\frac{1}{x^{2} - 4},\frac{x}{4 - 2x}$；
(8) $\frac{1}{x - 1},\frac{1}{x^{2} - 1},\frac{1}{x^{2} + x}$。
答案：2. 解: (1) $\frac{3}{x + 1} = \frac{3(x + 2)}{(x + 1)(x + 2)}, \frac{2}{x + 2} = \frac{2(x + 1)}{(x + 1)(x + 2)}$.
(2) $\frac{b}{a - x} = \frac{by}{ay - xy}, \frac{c}{ay - xy}$.
(3) $\frac{x + 1}{x^{2} - x} = \frac{x + 1}{x(x - 1)} = \frac{(x + 1)^{2}}{x(x - 1)(x + 1)}$,
$\frac{x - 1}{x^{2} + x} = \frac{x - 1}{x(x + 1)} = \frac{(x - 1)^{2}}{x(x + 1)(x - 1)}$.
(4) $\frac{2}{9 - 3a} = -\frac{2(a + 3)}{3(a - 3)(a + 3)}, \frac{a - 1}{a^{2} - 9} = \frac{3(a - 1)}{3(a - 3)(a + 3)}$.
(5) $\frac{2a}{a^{2} - 9} = \frac{2a(a - 3)}{(a - 3)^{2}(a + 3)}, \frac{3}{a^{2} - 6a + 9} = \frac{3(a + 3)}{(a - 3)^{2}(a + 3)}$.
(6) $\frac{1}{x + 1} = \frac{(x + 1)(x - 1)}{(x + 1)^{2}(x - 1)}, \frac{x - 1}{x^{2} + 2x + 1} = \frac{(x - 1)^{2}}{(x + 1)^{2}(x - 1)}$,
$\frac{1}{x - 1} = \frac{(x + 1)^{2}}{(x + 1)^{2}(x - 1)}$.
(7) $\frac{1}{x^{2} - 4} = \frac{1}{(x + 2)(x - 2)} = \frac{2}{2(x + 2)(x - 2)}$,
$\frac{x}{4 - 2x} = -\frac{x}{2(x - 2)} = -\frac{x(x + 2)}{2(x + 2)(x - 2)}$.
(8) $\frac{1}{x - 1} = \frac{x(x + 1)}{x(x + 1)(x - 1)}, \frac{1}{x^{2} - 1} = \frac{x}{x(x + 1)(x - 1)}$,
$\frac{1}{x^{2} + x} = \frac{x - 1}{x(x + 1)(x - 1)}$.
