Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 1325

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\[1)\ \frac{3}{x + 3} - \frac{2}{x - 3} = \frac{4}{x^{2} - 9}\]

\[3(x - 3) - 2(x + 3) = 4\]

\[3x - 9 - 2x - 6 = 4\]

\[x - 15 = 4\]

\[x = 19.\]

\[Ответ:\ \ x = 19.\]

\[2)\ \frac{5}{x - 2} + \frac{2}{x - 4} = \frac{11}{x^{2} - 6x + 8}\]

\[x^{2} - 6x + 8 = 0\]

\[D = 36 - 32 = 4\]

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

\[x_{2} = \frac{6 + 2}{2} = 4;\]

\[(x - 2)(x - 4) = 0.\]

\[5(x - 4) + 2(x - 2) = 11\]

\[5x - 20 + 2x - 4 = 11\]

\[7x - 24 = 11\]

\[7x = 35\]

\[x = 5.\]

\[Ответ:\ \ x = 5.\]