Решите уравнение: x^2/(x-5)+4x/(5-x)=5/(x-5).

\[\frac{x^{2}}{x - 5} + \frac{4x}{5 - x} = \frac{5}{x - 5}\]

\[\frac{x^{2}}{x - 5} - \frac{4x}{x - 5} - \frac{5}{x - 5} = 0\]

\[\frac{x^{2} - 4x - 5}{x - 5} = 0\ \ \ \ \ \ \ \ x \neq 5\]

\[x^{2} - 4x - 5 = 0\]

\[D = ( - 4)^{2} - 4 \cdot 1 \cdot ( - 5) =\]

\[= 16 + 20 = 36\]

\[x_{1} = \frac{4 + \sqrt{36}}{2} = \frac{4 + 6}{2} = \frac{10}{2} =\]

\[= 5\ (не\ подходит)\]

\[x_{2} = \frac{4 - \sqrt{36}}{2} = \frac{4 - 6}{2} = \frac{- 2}{2} =\]

\[= - 1.\]

\[Ответ:\ - 1.\]