Найдите корни уравнения: x/(x+1)+(x+2)/(x+6)-(8-2x)/(x^2+7x+6)=0.

\[\frac{x}{x + 1} + \frac{x + 2}{x + 6} - \frac{8 - 2x}{x^{2} + 7x + 6} = 0\]

\[x^{2} + 7x + 6 = 0\]

\[x_{1} + x_{2} = - 7;\ \ \ x_{1} \cdot x_{2} = 6\]

\[x_{1} = - 6;\ \ \ x_{2} = - 1.\]

\[2x^{2} + 11x - 6 = 0\]

\[D = 121 + 48 = 169\]

\[x_{1} = \frac{- 11 + 13}{4} = \frac{2}{4} = 0,5;\ \ \ \]

\[x_{2} = \frac{- 11 - 13}{4} = - \frac{24}{4} = - 6.\]

\[Ответ:x = 0,5;\ \ x = - 6.\]