Решебник по алгебре и начала математического анализа 10 класс Алимов Задание 147

\[\boxed{\mathbf{147.}}\]

\[\frac{1}{3x + 1} - \frac{2}{3x - 1} - \frac{5x}{9x^{2} - 1} =\]

\[= \frac{3x^{2}}{1 - 9x^{2}}\]

\[\frac{3x^{2} - 8x - 3}{9x^{2} - 1} = 0;\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \]

\[9x^{2} \neq 1;\ \ \ x \neq \pm \frac{1}{3}\]

\[3x^{2} - 8x - 3 = 0\]

\[D = 8^{2} + 4 \bullet 3 \bullet 3 =\]

\[= 64 + 36 = 100\]

\[x_{1} = \frac{8 - 10}{2 \bullet 3} = - \frac{2}{6} = - \frac{1}{3}\]

\[x_{2} = \frac{8 + 10}{2 \bullet 3} = \frac{18}{6} = 3.\]

\[Ответ:\ \ x = 3.\]