8. 分式$\dfrac{a}{a^{2} - b^{2}}$，$\dfrac{b}{a^{2} + 2ab + b^{2}}$，$\dfrac{c}{a^{2} - 2ab + b^{2}}$的最简公分母是.

8. $ (a - b)^{2}(a + b)^{2} $

9. 已知最简分式$\dfrac{1}{2y^{a}}$与$\dfrac{-1}{bxy}$($a$，$b$是常数，且$b ≠ 0$)的最简公分母为$10xy^{3}$，则$a$的值为，$b$的值为.

9. 3 5或10

3；5或10

10. 通分：
(1) $\dfrac{a + b}{(a + 2b)(a - 2b)}$，$\dfrac{a + b}{(2b + a)(2b - a)}$；
(2) $\dfrac{a}{a^{2} - 4a + 4}$，$\dfrac{b}{2a^{2} - 8a + 8}$，$\dfrac{c}{2a - 4}$；

(3) $\dfrac{2m}{9m + 15n}$，$\dfrac{3n}{6m - 10n}$，$\dfrac{2m + 5}{25n^{2} - 9m^{2}}$；
(4) $\dfrac{x}{x - y}$，$\dfrac{y}{x^{2} + 2xy + y^{2}}$，$\dfrac{2}{y^{2} - x^{2}}$.

10. (1) $ \frac{a + b}{(a + 2b)(a - 2b)} $，$ -\frac{a + b}{(a + 2b)(a - 2b)} $ (2) $ \frac{2a}{2(a - 2)^{2}} $，$ \frac{b}{2(a - 2)^{2}} $，$ \frac{c(a - 2)}{2(a - 2)^{2}} $ (3) $ \frac{4m(3m - 5n)}{6(3m + 5n)(3m - 5n)} $，$ \frac{9n(3m + 5n)}{6(3m + 5n)(3m - 5n)} $，$ -\frac{6(2m + 5)}{6(3m + 5n)(3m - 5n)} $ (4) $ \frac{x(x + y)^{2}}{(x - y)(x + y)^{2}} $，$ \frac{y(x - y)}{(x - y)(x + y)^{2}} $，$ -\frac{2(x + y)}{(x - y)(x + y)^{2}} $

解：$\dfrac{x}{x - y}=\dfrac{x(x + y)^{2}}{(x - y)(x + y)^{2}}$，$\dfrac{y}{x^{2} + 2xy + y^{2}}=\dfrac{y(x - y)}{(x - y)(x + y)^{2}}$，$\dfrac{2}{y^{2} - x^{2}}=-\dfrac{2(x + y)}{(x - y)(x + y)^{2}}$

11. 已知分式$\dfrac{1}{3x^{2} - 3}$，$\dfrac{2}{x - 1}$.若$a$是这两个分式的分母的公因式，$b$是这两个分式的最简公分母，且$\dfrac{b}{a} = - 6$，试求这两个分式的值.

11. 根据题意，得 $ a = x - 1 $，$ b = 3(x + 1)(x - 1) $。$ \because \frac{b}{a} = -6 $，$ \therefore \frac{3(x + 1)(x - 1)}{x - 1} = -6 $，即 $ 3(x + 1) = -6 $，解得 $ x = -3 $。$ \therefore \frac{1}{3x^{2} - 3} = \frac{1}{3× (-3)^{2} - 3} = \frac{1}{24} $，$ \frac{2}{x - 1} = \frac{2}{-3 - 1} = -\frac{1}{2} $