Найдите корни уравнения: (2x-7)/(x-4)-(x+2)/(x+1)=(x+6)/(x-4)(x+1).

Ответ:

\[\frac{2x - 7}{x - 4} - \frac{x + 2}{x + 1} = \frac{x + 6}{(x - 4)(x + 1)}\]

\[ОДЗ:\ \ x \neq - 1\]

\[\ \ \ \ \ \ \ \ \ \ \ x \neq 4\]

\[\frac{(2x - 7)(x + 1) - (x + 2)(x - 4)}{(x - 4)(x + 1)} =\]

\[= \frac{x + 6}{(x - 4)(x + 1)}\]

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

\[x_{1} + x_{2} = 4\]

\[x_{1} \cdot x_{2} = - 5 \Longrightarrow x_{1} = 5;\ \ \]

\[x_{2} = - 1\ (не\ подходит\ по\ ОДЗ)\]

\[Ответ:x = 5.\]