32 ж) x3 - 2x2 - x + 2 + (x - 1)(x - 2) = x + 1 1 1 1

Ответ:

\[\frac{32}{x^3 - 2x^2 - x + 2} + \frac{1}{(x - 1)(x - 2)} = \frac{1}{x + 1}\]

\[\frac{32}{x^2(x - 2) - (x - 2)} + \frac{1}{(x - 1)(x - 2)} = \frac{1}{x + 1}\]

\[\frac{32}{(x - 2)(x^2 - 1)} + \frac{1}{(x - 1)(x - 2)} = \frac{1}{x + 1}\]

\[\frac{32}{(x - 2)(x - 1)(x + 1)} + \frac{1}{(x - 1)(x - 2)} = \frac{1}{x + 1}\]

Общий знаменатель: \[(x - 2)(x - 1)(x + 1)\]

\[\frac{32 + (x + 1)}{(x - 2)(x - 1)(x + 1)} = \frac{(x - 2)(x - 1)}{(x - 2)(x - 1)(x + 1)}\]

\[32 + x + 1 = (x - 2)(x - 1)\]

\[33 + x = x^2 - 3x + 2\]

\[x^2 - 4x - 31 = 0\]

\[D = (-4)^2 - 4 \cdot 1 \cdot (-31) = 16 + 124 = 140\]

\[x = \frac{4 \pm \sqrt{140}}{2} = \frac{4 \pm 2\sqrt{35}}{2} = 2 \pm \sqrt{35}\]

Ответ: \[x = 2 \pm \sqrt{35}\]