Алгебра
Английский
Биология
География
Геометрия
История
Русский
Обществознание
Физика
Химия
Информатика
Литература
МатематикаРешебник по алгебре 8 класс Мерзляк ФГОС Задание 218
Задание 218
\[\boxed{\text{218}\text{\ (218)}\text{.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\ \frac{4y + 24}{5y^{2} - 45} + \frac{y + 3}{5y^{2} - 15y} =\]
\[= \frac{y - 3}{y^{2} + 3y}\]
\[\frac{4y + 24^{\backslash y}}{5 \cdot (y - 3)(y + 3)} + \frac{y + 3^{\backslash y + 3}}{5y(y - 3)} -\]
\[- \frac{y - 3^{\backslash 5(y - 3)}}{y(y + 3)} = 0\]
\[\frac{60y - 36}{5y(y - 3)(y + 3)} = 0\]
\[\left\{ \begin{matrix} 60y - 36 = 0 \\ y \neq 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ y \neq 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ y \neq - 3\ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} y = \frac{6}{10}\text{\ \ } \\ y \neq 0\ \ \ \ \ \\ y \neq 3\ \ \ \ \ \\ y \neq - 3\ \\ \end{matrix} \right.\ \]
\[Ответ:y = 0,6.\]
\[2)\ \frac{y + 2}{8y^{3} + 1} - \frac{1}{4y + 2} =\]
\[= \frac{y + 3}{8y^{2} - 4y + 2}\]
\[\frac{y + 2^{\backslash 2}}{(2y + 1)\left( 4y^{2} - 2y + 1 \right)} -\]
\[- \frac{1^{\backslash 4y^{2} - 2y + 1}}{2 \cdot (2y + 1)} -\]
\[- \frac{y + 3^{\backslash 2y + 1}}{2 \cdot \left( 4y^{2} - 2y + 1 \right)} = 0\]
\[\frac{- 6y^{2} - 3y}{2 \cdot (2y + 1)\left( 4y^{2} - 2y + 1 \right)} = 0\]
\[\frac{- 3y(2y + 1)}{2 \cdot (2y + 1)\left( 4y^{2} - 2y + 1 \right)} = 0\]
\[4y^{2} - 2y + 1 = 0\]
\[D_{1} = 1 - 4 = - 3 < 0 - корней\ \]
\[нет.\]
\[\left\{ \begin{matrix} y = 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ y = - 0,5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ y \neq - 0,5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 4y^{2} - 2y + 1 \neq 0\ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} y = 0\ \ \ \ \ \ \ \\ y \neq - 0,5 \\ \end{matrix} \right.\ \]
\[Ответ:y = 0.\]
\[\boxed{\text{218.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\ \frac{x - 1}{x - a} = 0\]
\[если\ a \neq 1:\]
\[x - 1 = 0\]
\[\ x = 1.\]
\[если\ a = 1:\]
\[\frac{x - 1}{x - 1} = 0\ \ \]
\[1 \neq 0 - корней\ нет.\]
\[2)\ \frac{x - a}{x + 5} = 0\]
\[если\ a \neq - 5:\]
\[\left\{ \begin{matrix} x - a = 0 \\ x \neq - 5\ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ }\]
\[x = a.\]
\[если\ a = - 5:\]
\[\frac{x + 5}{x + 5} = 0\ \ \]
\[1 \neq 0 - корней\ нет.\]
\[3)\ \frac{a(x - a)}{x - 3} = 0\]
\[если\ a = 0:\ \]
\[\frac{0}{x - 3} = 0\ \ \]
\[\left\{ \begin{matrix} x - любое\ число \\ x \neq 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ .\]
\[если\ a \neq 0;\ \ a \neq 3\]
\[\left\{ \begin{matrix} x - a = 0 \\ x - 3 \neq 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = a \\ x \neq 3 \\ \end{matrix} \right.\ \ \]
\[x = a.\]
\[если\ a = 3:\]
\[\frac{3(x - 3)}{x - 3} = 0\]
\[1 \neq 0 - корней\ нет.\]
\[4)\ \frac{(x - a)(x - 6)}{x - 7} = 0\]
\[если\ a \neq 7:\]
\[\left\{ \begin{matrix} x - a = 0 \\ x - 6 = 0 \\ x \neq 7\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ }\]
\[\left\{ \begin{matrix} x = a \\ x \neq 7 \\ \end{matrix} \right.\ \ \]
\[x = a\ или\ x = 6.\]
\[если\ a = 7:\]
\[\frac{(x - 7)(x - 6)}{x - 7} = 0\ \ \]
\[\left\{ \begin{matrix} x = 6 \\ x \neq 7 \\ \end{matrix} \right.\ \text{\ \ }\]
\[x = 6.\]
\[5)\ \frac{(x - 4)(x + 2)}{x - a} = 0\]
\[если\ a \neq 4\ и\ a \neq - 2:\]
\[\left\{ \begin{matrix} x - 4 = 0 \\ x + 2 = 0 \\ \end{matrix} \right.\ \]
\[x = 4\ или\ x = - 2.\]
\[если\ a = 4:\ \ \]
\[\frac{(x - 4)(x + 2)}{(x - 4)} = 0\ \ \]
\[x + 2 = 0\ \ \]
\[x = - 2.\]
\[если\ a = - 2:\]
\[\frac{(x - 4)(x + 2)}{x + 2} = 0\ \ \]
\[x - 4 = 0\]
\[x = 4.\]
\[6)\ \frac{x - a}{(x - 4)(x + 2)} = 0\]
\[если\ a \neq 4\ и\ a \neq - 2:\]
\[\left\{ \begin{matrix} x - a = 0 \\ x \neq 4\ \ \ \ \ \ \ \\ x \neq - 2\ \ \ \ \\ \end{matrix} \right.\ \]
\[x = a.\]
\[если\ a = 4:\ \]
\[\frac{x - 4}{(x - 4)(x + 2)} = 0\]
\[\left\{ \begin{matrix} x - 4 = 0 \\ x \neq 4\ \ \ \ \ \ \ \ \\ x \neq - 2\ \ \ \ \\ \end{matrix}\ \right.\ \text{\ \ \ }\left\{ \begin{matrix} x = 4\ \ \ \\ x \neq 4\ \ \ \\ x \neq - 2\ \\ \end{matrix} \right.\ \]
\[корней\ нет.\]
\[если\ a = - 2:\]
\[\frac{x + 2}{(x - 4)(x + 2)} = 0\ \]
\[\left\{ \begin{matrix} x + 2 = 0 \\ x \neq 4\ \ \ \ \ \ \ \ \\ x \neq - 2\ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ }\left\{ \begin{matrix} x = - 2 \\ x \neq 4\ \ \ \\ x \neq - 2 \\ \end{matrix} \right.\ \]
\[корней\ нет.\]
