ГДЗ по алгебре 8 класс Мерзляк Задание 208

\[\boxed{\text{208\ (208).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

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

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

\[\left\{ \begin{matrix} (x - 1)(x + 1) = 0 \\ (x - 1)^{2} \neq 0\ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 1\ \ \ \\ x = - 1 \\ x \neq 1\ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:\ x = - 1.\]

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

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

\[\left\{ \begin{matrix} (x - 1)^{2} = 0 \\ x^{2} - 1 \neq 0\ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x \neq 1\ \ \\ x \neq - 1 \\ x = 1\ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:нет\ корней.\]

\[3)\ \frac{x + 7}{x - 7} - \frac{2x - 3}{x - 7} = 0\]

\[\frac{x + 7 - 2x + 3}{x - 7} = 0\]

\[\frac{- x + 10}{x - 7} = 0\]

\[\left\{ \begin{matrix} x = 10 \\ x \neq 7\ \ \\ \end{matrix} \right.\ \]

\[Ответ:x = 10.\]

\[4)\ \frac{10 - 3x}{x + 8} + \frac{5x + 6}{x + 8} = 0\]

\[\frac{10 - 3x + 5x + 6}{x + 8} = 0\]

\[\frac{2x + 16}{x + 8} = 0\]

\[\left\{ \begin{matrix} 2x + 16 = 0 \\ x \neq - 8\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = - 8 \\ x \neq - 8 \\ \end{matrix} \right.\ \]

\[Ответ:нет\ корней.\]

\[5)\ \frac{x - 6^{\backslash x}}{x - 2} - \frac{x - 8^{\backslash x - 2}}{x} = 0\]

\[\frac{x^{2} - 6x - x^{2} + 8x + 2x - 16}{x(x - 2)} = 0\]

\[\frac{4x - 16}{x(x - 2)} = 0\]

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

\[Ответ:x = 4.\]

\[6)\ \frac{2x - 4}{x} - \frac{3x + 1}{x} + \frac{x + 5}{x} = 0\]

\[\frac{2x - 4 - 3x - 1 + x + 5}{x} = 0\]

\[\left\{ \begin{matrix} \frac{0}{x} = 0 \\ x \neq 0 \\ \end{matrix} \right.\ \]

\[Ответ:x \in ( - \infty;0) \cup (0; + \infty).\]

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

\[\frac{x^{\backslash x}}{x + 6} - \frac{36}{x(x + 6)} = 0\]

\[\frac{x^{2} - 36}{x(x + 6)} = 0\]

\[\left\{ \begin{matrix} x^{2} = 36 \\ x \neq 0\ \ \ \ \ \\ x \neq - 6\ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 6\ \ \ \\ x = - 6 \\ x \neq 0\ \ \ \\ x \neq - 6 \\ \end{matrix} \right.\ \]

\[Ответ:x = 6.\]

\[8)\ \frac{2x^{2} + 3x + 1}{2x + 1} - x = 1\]

\[\frac{2x^{2} + 3x + 1}{2x + 1} - x^{\backslash 2x + 1} -\]

\[- 1^{\backslash 2x + 1} = 0\]

\[\frac{2x^{2} + 3x + 1 - 2x^{2} - x - 2x - 1}{2x + 1} = 0\]

\[\frac{0}{2x + 1} = 0\]

\[2x + 1 \neq 0\]

\[x \neq - 0,5\]

\[Ответ:x \in\]

\[\in ( - \infty;\ - 0,5) \cup ( - 0,5;\ + \infty).\]

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

\[\frac{4^{\backslash x + 1}}{x - 1} - \frac{4^{\backslash x - 1}}{x + 1} - 1^{\backslash x^{2} - 1} = 0\]

\[\frac{4x + 4 - 4x + 4 - x^{2} + 1}{x^{2} - 1} = 0\]

\[\frac{9 - x^{2}}{(x - 1)(x + 1)} = 0\]

\[\left\{ \begin{matrix} - x^{2} + 9 = 0 \\ x \neq 1\ \ \ \ \ \ \ \ \ \ \ \ \\ x \neq - 1\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 3\ \ \ \\ x = - 3 \\ x \neq 1\ \ \ \\ x \neq - 1 \\ \end{matrix} \right.\ \]

\[Ответ:x = 3;\ x = - 3.\]