Решебник по алгебре 8 класс Мерзляк Задание 213

\[\boxed{\text{213\ (213).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ \frac{x - 2}{x + 1} - \frac{5}{1 - x} = \frac{x^{2} + 27}{x^{2} - 1}\]

\[\frac{x - 2^{\backslash x - 1}}{x + 1} + \frac{5^{\backslash x + 1}}{x - 1} -\]

\[- \frac{x^{2} + 27}{(x - 1)(x + 1)} = 0\]

\[\frac{2x - 20}{(x + 1)(x - 1)} = 0\]

\[\left\{ \begin{matrix} 2x - 20 = 0 \\ x \neq - 1\ \ \ \ \ \ \ \ \ \\ x \neq 1\ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 10 \\ x \neq - 1 \\ x \neq 1\ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:x = 10.\]

\[2)\ \frac{3x + 1}{3x - 1} - \frac{3x - 1}{3x + 1} = \frac{6}{1 - 9x^{2}}\]

\[\frac{3x + 1^{\backslash 3x + 1}}{3x - 1} - \frac{3x - 1^{\backslash 3x - 1}}{3x + 1} +\]

\[+ \frac{6}{(3x - 1)(3x + 1)} = 0\]

\[\frac{12x + 6}{(3x - 1)(3x + 1)} = 0\]

\[\left\{ \begin{matrix} 12x + 6 = 0 \\ x \neq \frac{1}{3}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ } \\ x \neq - \frac{1}{3}\text{\ \ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = - 0,5 \\ x \neq \frac{1}{3}\text{\ \ \ \ \ \ \ } \\ x \neq - \frac{1}{3}\text{\ \ } \\ \end{matrix} \right.\ \]

\[Ответ:\ x = - 0,5.\]

\[3)\ \frac{4}{x - 3} + \frac{1}{x} = \frac{5}{x - 2}\]

\[\frac{4^{\backslash x(x - 2)}}{x - 3} + \frac{1^{\text{(}x - 3)(x - 2)}}{x} -\]

\[- \frac{5^{\backslash x(x - 3)}}{x - 2} = 0\]

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

\[\left\{ \begin{matrix} 2x + 6 = 0 \\ x \neq 0\ \ \ \ \ \ \ \ \ \ \\ x \neq 3\ \ \ \ \ \ \ \ \ \ \\ x \neq 2\ \ \ \ \ \ \ \ \ \\ \end{matrix}\ \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = - 3 \\ x \neq 0\ \ \ \\ x \neq 3\ \ \ \\ x \neq 2\ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:\ x = - 3.\]

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

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

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

\[\frac{x^{2} - 16}{(x - 2)(x + 2)} = 0\]

\[\left\{ \begin{matrix} x^{2} - 16 = 0 \\ x \neq 2\ \ \ \ \ \ \ \ \ \ \ \ \\ x \neq - 2\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 4\ \ \ \\ x = - 4 \\ x \neq 2\ \ \ \ \\ x \neq - 2 \\ \end{matrix} \right.\ \]

\[Ответ:x = 4;\ x = - 4.\]

\[5)\ \frac{7}{x^{2} + 2x} + \frac{x + 1}{x^{2} - 2x} = \frac{x + 4}{x^{2} - 4}\]

\[\frac{7^{\backslash x - 2}}{x(x + 2)} + \frac{x + 1^{\backslash x + 2}}{x(x - 2)} -\]

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

\[\frac{6x - 12}{x(x + 2)(x - 2)} = 0\]

\[\left\{ \begin{matrix} 6x - 12 = 0 \\ x \neq 0\ \ \ \ \ \ \ \ \ \ \ \ \ \\ x \neq - 2\ \ \ \ \ \ \ \ \ \ \\ x \neq 2\ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 2\ \ \ \\ x \neq 0\ \ \ \\ x \neq - 2 \\ x \neq 2\ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:нет\ корней.\]

\[6)\ \frac{x^{2} - 9x + 50}{x^{2} - 5x} = \frac{x + 1}{x - 5} + \frac{x - 5}{x}\]

\[\frac{x^{2} - 9x + 50}{x(x - 5)} - \frac{x + 1^{\backslash x}}{x - 5} -\]

\[- \frac{x - 5^{\backslash x - 5}}{x} = 0\]

\[\frac{- x^{2} + 25}{x(x - 5)} = 0\]

\[\left\{ \begin{matrix} {- x}^{2} + 25 = 0 \\ x \neq 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x \neq 5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 5\ \ \ \\ x = - 5 \\ x \neq 0\ \ \ \\ x \neq 5\ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:\ x = - 5.\ \]