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МатематикаРешебник по алгебре 8 класс Мерзляк ФГОС Задание 207
Задание 207
\[\boxed{\text{207\ (207).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\frac{x - 6}{x - 4} = 0\]
\[\left\{ \begin{matrix} x - 6 = 0\ \\ x - 4 \neq 0\ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 6\ \\ x \neq 4\ \\ \end{matrix} \right.\ \]
\[Ответ:x = 6.\]
\[2)\ \frac{x - 2}{x^{2} - 4} = 0\]
\[\left\{ \begin{matrix} x - 2 = 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ (x - 2)(x + 2) \neq 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x = 2\ \ \ \\ x \neq 2\ \ \ \\ x \neq - 2 \\ \end{matrix} \right.\ \]
\[Ответ:нет\ корней.\]
\[3)\ \frac{x^{2} - 4}{x - 2} = 0\]
\[\left\{ \begin{matrix} (x - 2)(x + 2) = 0 \\ x - 2 \neq 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 2\ \ \ \\ x = - 2 \\ x \neq 2\ \ \ \\ \end{matrix} \right.\ \]
\[Ответ:\ x = - 2.\]
\[4)\ \frac{x - 2}{x - 2} = 1\]
\[\left\{ \begin{matrix} x \neq 2 \\ 1 = 1 \\ \end{matrix} \right.\ \]
\[Ответ:x \in ( - \infty;2)\ \cup (2; + \infty).\]
\[5)\ \frac{2x^{2} + 18}{x^{2} + 9} = 2;\ \ \ x^{2} + 9 \neq 0\]
\[\frac{2 \cdot \left( x^{2} + 9 \right)}{x^{2} + 9} = 2\]
\[2 = 2\]
\[Ответ:x \in ( - \infty; + \infty).\]
\[6)\ \frac{x}{x - 5} + \frac{2x - 9}{x - 5} = 0\]
\[\frac{x + 2x - 9}{x - 5} = 0\]
\[\frac{3x - 9}{x - 5} = 0\]
\[\left\{ \begin{matrix} 3x - 9 = 0 \\ x - 5 \neq 0\ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x = 3 \\ x \neq 5 \\ \end{matrix} \right.\ \]
\[Ответ:x = 3.\]
\[7)\ \frac{5x - 7}{x + 1} - \frac{x - 5}{x + 1} = 0\]
\[\frac{5x - 7 - x + 5}{x + 1} = 0\]
\[\frac{4x - 2}{x + 1} = 0\]
\[\left\{ \begin{matrix} 4x - 2 = 0 \\ x + 1 \neq 0\ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 0,5 \\ x \neq - 1 \\ \end{matrix} \right.\ \]
\[Ответ:x = 0,5.\]
\[8)\ \frac{2x + 16}{x + 3} - \frac{1 - 3x}{x + 3} = 0\]
\[\frac{2x + 16 - 1 + 3x}{x + 3} = 0\]
\[\frac{5x + 15}{x + 3} = 0\]
\[\left\{ \begin{matrix} 5x + 15 = 0 \\ x + 3 \neq 0\ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = - 3 \\ x \neq - 3 \\ \end{matrix} \right.\ \]
\[Ответ:нет\ корней.\]
\[9)\ \frac{2^{\backslash x + 1}}{x - 1} + \frac{1^{\backslash x - 1}}{x + 1} = 0\]
\[\frac{2x + 2 + x - 1}{(x - 1)(x + 1)} = 0\]
\[\frac{3x + 1}{(x - 1)(x + 1)} = 0\]
\[\left\{ \begin{matrix} 3x + 1 = 0 \\ x \neq 1\ \ \ \ \ \ \ \ \ \ \\ x \neq - 1\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = - \frac{1}{3} \\ x \neq 1\ \ \ \ \\ x \neq - 1 \\ \end{matrix} \right.\ \]
\[Ответ:\ x = - \frac{1}{3}.\]
\[10)\ \frac{3}{x - 2} = \frac{4}{x + 3}\]
\[\frac{3^{\backslash x + 3}}{x - 2} - \frac{4^{\backslash x - 2}}{x + 3} = 0\]
\[\frac{3x + 9 - 4x + 8}{(x - 2)(x + 3)} = 0\]
\[\left\{ \begin{matrix} - x + 17 = 0 \\ x \neq 2\ \ \ \ \ \ \ \ \ \ \ \ \ \\ x \neq - 3\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 17 \\ x \neq 2\ \ \ \\ x \neq - 3 \\ \end{matrix} \right.\ \]
\[Ответ:x = 17.\]
\[11)\ \frac{x}{x - 6} = 2\]
\[\frac{x}{x - 6} - 2^{\backslash x - 6} = 0\]
\[\frac{x - 2x + 12}{x - 6} = 0\]
\[\left\{ \begin{matrix} - x + 12 = 0 \\ x - 6 \neq 0\ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 12 \\ x \neq 6\ \ \ \\ \end{matrix} \right.\ \]
\[Ответ:x = 12.\]
\[12)\ \frac{x - 4^{\backslash 2x - 1}}{x - 3} - \frac{2x + 1^{\backslash x - 3}}{2x - 1} = 0\]
\[\frac{2x^{2} - 8x - x + 4 - 2x^{2} - x + 6x + 3}{(x - 3)(2x - 1)} = 0\]
\[\frac{- 4x + 7}{(x - 3)(2x - 1)} = 0\]
\[\left\{ \begin{matrix} - 4x + 7 = 0 \\ x \neq 3\ \ \ \ \ \ \ \ \ \ \ \ \ \\ x \neq 0,5\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 1\frac{3}{4} \\ x \neq 3\ \ \ \ \\ x \neq 0,5 \\ \end{matrix} \right.\ \]
\[Ответ:x = 1\frac{3}{4}.\]
\[13)\ \frac{x + 8^{\backslash x - 2}}{x} - \frac{6^{\backslash x}}{x - 2} = 0\]
\[\frac{x^{2} + 8x - 2x - 16 - 6x}{x(x - 2)} = 0\]
\[\left\{ \begin{matrix} x^{2} - 16 = 0 \\ x \neq 0\ \ \ \ \ \ \ \ \ \ \ \ \\ x \neq 2\ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 4\ \ \ \\ x = - 4 \\ x \neq 0\ \ \ \\ x \neq 2\ \ \ \\ \end{matrix} \right.\ \]
\[Ответ:x = 4;\ x = - 4.\]
\[14)\ \frac{2x^{\backslash x + 5}}{x - 5} - \frac{x^{2} + 15x}{x^{2} - 25} = 0\]
\[\frac{2x^{2} + 10x - x^{2} - 15x}{(x - 5)(x + 5)} = 0\]
\[\left\{ \begin{matrix} x(x - 5) = 0 \\ x \neq 5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x \neq - 5\ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 0\ \ \ \\ x = 5\ \ \ \\ x \neq 5\ \ \ \\ x \neq - 5 \\ \end{matrix} \right.\ \]
\[Ответ:\ \ x = 0.\]
\[15)\ 3^{\backslash x^{2} - 3x} - \frac{2x^{2} - 5x}{x^{2} - 3x} = 0\]
\[\frac{{3x}^{2} - 9x - 2x^{2} + 5x}{x(x - 3)} = 0\ \]
\[\left\{ \begin{matrix} x(x - 4) = 0 \\ x \neq 0\ \ \ \ \ \ \ \ \ \ \ \ \ \\ x \neq 3\ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 0 \\ x = 4 \\ x \neq 0 \\ x \neq 3 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]
\[Ответ:x = 4.\]
\[\boxed{\text{207.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\frac{x^{2} - 1}{x^{2} - 2x + 1} = 0\]
\[\frac{(x - 1)(x + 1)}{(x - 1)^{2}} = 0\]
\[\left\{ \begin{matrix} (x - 1)(x + 1) = 0 \\ (x - 1)^{2} \neq 0\ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 1\ \ \ \\ x = - 1 \\ x \neq 1\ \ \ \\ \end{matrix} \right.\ \]
\[Ответ:\ x = - 1.\]
\[2)\ \frac{x^{2} - 2x + 1}{x^{2} - 1} = 0\]
\[\frac{(x - 1)^{2}}{x^{2} - 1} = 0\]
\[\left\{ \begin{matrix} (x - 1)^{2} = 0 \\ x^{2} - 1 \neq 0\ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x \neq 1\ \ \\ x \neq - 1 \\ x = 1\ \ \ \\ \end{matrix} \right.\ \]
\[Ответ:нет\ корней.\]
\[3)\ \frac{x + 7}{x - 7} - \frac{2x - 3}{x - 7} = 0\]
\[\frac{x + 7 - 2x + 3}{x - 7} = 0\]
\[\frac{- x + 10}{x - 7} = 0\]
\[\left\{ \begin{matrix} x = 10 \\ x \neq 7\ \ \\ \end{matrix} \right.\ \]
\[Ответ:x = 10.\]
\[4)\ \frac{10 - 3x}{x + 8} + \frac{5x + 6}{x + 8} = 0\]
\[\frac{10 - 3x + 5x + 6}{x + 8} = 0\]
\[\frac{2x + 16}{x + 8} = 0\]
\[\left\{ \begin{matrix} 2x + 16 = 0 \\ x \neq - 8\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = - 8 \\ x \neq - 8 \\ \end{matrix} \right.\ \]
\[Ответ:нет\ корней.\]
\[5)\ \frac{2x - 4}{x} - \frac{3x + 1}{x} + \frac{x + 5}{x} = 0\]
\[\frac{2x - 4 - 3x - 1 + x + 5}{x} = 0\]
\[\left\{ \begin{matrix} \frac{0}{x} = 0 \\ x \neq 0 \\ \end{matrix} \right.\ \]
\[Ответ:x \in ( - \infty;0) \cup (0; + \infty).\]
\[6)\ \frac{x}{x + 6} - \frac{36}{x^{2} + 6x} = 0\]
\[\frac{x^{\backslash x}}{x + 6} - \frac{36}{x(x + 6)} = 0\]
\[\frac{x^{2} - 36}{x(x + 6)} = 0\]
\[\left\{ \begin{matrix} x^{2} = 36 \\ x \neq 0\ \ \ \ \ \\ x \neq - 6\ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 6\ \ \ \\ x = - 6 \\ x \neq 0\ \ \ \\ x \neq - 6 \\ \end{matrix} \right.\ \]
\[Ответ:x = 6.\]
\[7)\ \frac{2x^{2} + 3x + 1}{2x + 1} - x = 1\]
\[\frac{2x^{2} + 3x + 1}{2x + 1} - x^{\backslash 2x + 1} -\]
\[- 1^{\backslash 2x + 1} = 0\]
\[\frac{2x^{2} + 3x + 1 - 2x^{2} - x - 2x - 1}{2x + 1} = 0\]
\[\frac{0}{2x + 1} = 0\]
\[2x + 1 \neq 0\]
\[x \neq - 0,5\]
\[Ответ:x \in\]
\[\in ( - \infty;\ - 0,5) \cup ( - 0,5;\ + \infty).\]
\[8)\ \frac{4}{x - 1} - \frac{4}{x + 1} = 1\]
\[\frac{4^{\backslash x + 1}}{x - 1} - \frac{4^{\backslash x - 1}}{x + 1} - 1^{\backslash x^{2} - 1} = 0\]
\[\frac{4x + 4 - 4x + 4 - x^{2} + 1}{x^{2} - 1} = 0\]
\[\frac{9 - x^{2}}{(x - 1)(x + 1)} = 0\]
\[\left\{ \begin{matrix} - x^{2} + 9 = 0 \\ x \neq 1\ \ \ \ \ \ \ \ \ \ \ \ \\ x \neq - 1\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 3\ \ \ \\ x = - 3 \\ x \neq 1\ \ \ \\ x \neq - 1 \\ \end{matrix} \right.\ \]
\[Ответ:x = 3;\ x = - 3.\]
