Решите уравнение: x^2/(x-2)-x/(2-x)=6/(x-2).

\[\frac{x^{2}}{x - 2} - \frac{x}{2 - x} = \frac{6}{x - 2}\]

\[\frac{x^{2}}{x - 2} + \frac{x}{x - 2} - \frac{6}{x - 2} = 0\]

\[\frac{x^{2} + x - 6}{x - 2} = 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ x \neq 2\]

\[x^{2} + x - 6 = 0\]

\[D = 1^{2} - 4 \cdot 1 \cdot ( - 6) = 1 + 24 =\]

\[= 25\]

\[x_{1} = \frac{- 1 + \sqrt{25}}{2} = \frac{- 1 + 5}{2} = \frac{4}{2} =\]

\[= 2\ (не\ подходит)\]

\[x_{2} = \frac{- 1 - \sqrt{25}}{2} = \frac{- 1 - 5}{2} =\]

\[= \frac{- 6}{2} = - 3\]

\[Ответ:\ - 3.\]