Решите уравнение: (x^2-1)/(x+5)=(5-x)/(x+5).

\[\frac{x^{2} - 1}{x + 5} = \frac{5 - x}{x + 5}\]

\[ОДЗ:\ \ x \neq - 5\]

\[\frac{x^{2} - 1 - 5 + x}{x + 5} = 0\]

\[\frac{x^{2} + x - 6}{x + 5} = 0\]

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

\[x_{1} + x_{2} = - 1\]

\[x_{1} \cdot x_{2} = - 6 \Longrightarrow x_{1} = - 3;\ \ \ \]

\[x_{2} = 2\ \]

\[Ответ:\ \ x = - 3\ \ \ \ и\ \ \ x = 2.\]