ГДЗ по алгебре 8 класс Мерзляк Задание 369

\[\boxed{\text{369\ (369).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\frac{6}{x - 2} - \frac{x + 3}{x} = \frac{x + 6}{x^{2} - 2x}\]

\[\frac{6^{\backslash x}}{x - 2} - \frac{x + 3^{\backslash x - 2}}{x} -\]

\[- \frac{x + 6}{x(x - 2)} = 0\]

\[\frac{6 \cdot x - (x + 3)(x - 2) - (x + 6)}{x(x - 2)} = 0\]

\[\frac{6x - x^{2} + 2x - 3x + 6 - x - 6}{x(x - 2)} = 0\]

\[\frac{- x^{2} + 4x}{x(x - 2)} = 0\]

\[\frac{x( - x + 4)}{x(x - 2)} = 0\]

\[\left\{ \begin{matrix} x( - x + 4) = 0 \\ x(x - 2) \neq 0\ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} x = 0 \\ x = 4 \\ x \neq 0 \\ x \neq 2 \\ \end{matrix} \right.\ \ \ \ \ \ \ x = 4\]

\[Ответ:x = 4.\]