Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 1329

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\[1)\ \frac{x}{x + 1} + \frac{x}{x - 1} = 0\ \ \ \ \ | \bullet (x - 1)(x + 1)\]

\[x(x - 1) + x(x + 1) = 0\]

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

\[2x^{2} = 0\]

\[x = 0.\]

\[Ответ:\ \ x = 0.\]

\[2)\ \frac{3x^{2}}{3x + 1} - 2 = \frac{2x + 1}{3x + 1}\ \ \ \ \ | \bullet (3x + 1)\]

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

\[3x^{2} - 6x - 2 = 2x + 1\]

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

\[D = 64 + 36 = 100\]

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

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

\[ОДЗ:\]

\[3x + 1 \neq 0\]

\[3x \neq - 1\]

\[x \neq - \frac{1}{3}.\]

\[Ответ:\ \ x = 3.\]