Answer:
[tex]1) \frac{1}{(x - 3)(x + 2)} + \frac{3}{(x + 2)(4 - x)} + \frac{2}{(x - 3)(x - 4)} \\ \\ = \frac{x - 4}{(x - 3)(x + 2)(x - 4)} - \frac{3(x - 3)}{(x - 4)(x + 2)(x - 3)} + \frac{2(x + 2)}{(x + 2)(x - 3)(x - 4)} \\ \\ = \frac{x - 4 - 3x + 9 + 2x + 4}{(x - 3)(x - 4)(x + 2)} \\ \\ = \frac{9}{(x + 2)(x - 3)(x - 4)} [/tex]
[tex]2) \frac{2}{(x - 2)(x - 3)} + \frac{2}{(x - 1)(3 - x)} + \frac{1}{(1 - x)(2 - x)} \\ \\ = \frac{2(x - 1)}{(x - 1)(x - 2)(x - 3)} - \frac{2(x - 2)}{(x - 1)(x - 2)(x - 3)} + \frac{x - 3}{(x - 1)(x - 2)(x - 3)} \\ \\ = \frac{2x - 2 - 2x + 4 + x - 3}{(x - 1)(x -2)(x - 3)} \\ \\ = \frac{x - 1}{(x - 1)(x - 2)(x - 3)} \\ \\ = \frac{1}{(x - 2)(x - 3)} [/tex]
