ГДЗ по алгебре 9 класс Макарычев Задание 819

\[\boxed{\text{819\ (819).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ \frac{x}{x - 5} - \frac{4}{x + 5} + \frac{76}{25 - x^{2}} = 0\]

\[\frac{x}{x - 5} - \frac{4}{x + 5} - \frac{76}{x^{2} - 25} = 0,\]

\[x \neq \pm 5,\]

\[x(x + 5) - 4 \cdot (x - 5) - 76 = 0\]

\[x^{2} + 5x - 4x + 20 - 76 = 0\]

\[x^{2} + x - 56 = 0\]

\[D = 1 + 4 \cdot 56 = 225\]

\[x_{1,2} = \frac{- 1 \pm 15}{2},\]

\[x_{1} = 7,\ \ x_{2} = - 8.\]

\[Ответ:x = 7;x = - 8.\]

\[\textbf{б)}\ \frac{7x}{x² - 36} + \frac{3}{6 - x} = \frac{7}{x + 6}\]

\[\frac{7x}{x^{2} - 36} - \frac{3}{x - 6} - \frac{7}{x + 6} = 0,\]

\[x \neq \pm 6,\]

\[7x - 3 \cdot (x + 6) - 7 \cdot (x - 6) = 0\]

\[7x - 3x - 18 - 7x + 42 = 0\]

\[- 3x + 24 = 0\]

\[x = 8.\]

\[Ответ:x = 8.\]