Решебник по алгебре 8 класс Макарычев ФГОС Задание 1218

\[\boxed{\text{1218.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]

\[\frac{2x - 7}{x + 1} + \frac{3x + 2}{x - 1} = 7\]

\[\frac{(2x - 7)(x - 1) + (3x + 2)(x + 1)}{(x - 1)(x + 1)} = 7\]

\[2x^{2} - 2x - 7x + 7 + 3x^{2} + 3x +\]

\[+ 2x + 2 = 7 \cdot \left( x^{2} - 1 \right)\]

\[5x^{2} - 4x + 9 = 7x^{2} - 7\]

\[- 2x^{2} - 4x + 16 = 0\ \ \ \ |\ :( - 2)\]

\[x^{2} + 2x - 8 = 0\]

\[D = 4 + 32 = 36\]

\[x_{1,2} = \frac{- 2 \pm 6}{2} = 2;\ - 4\]

\[Ответ:\text{\ x}_{1} = 2;\ \ x_{2} = - 4.\]