номер 125 гдз 8 класс алгебра Муравин Муравин

1)\begin{equation}\frac{1}{4x-6}+\frac{2x-5}{18-8x^{2}}=\frac{1}{2x^{2}+3x} \end{equation} \begin{equation}\frac{1}{2\left ( 2x-3 \right )}+\frac{2x-5}{2\left ( 9-4x^{2} \right )}-\frac{1}{x\left ( 2x+3 \right )}=0 \end{equation} \begin{equation}\frac{1}{2\left ( 2x-3 \right )}-\frac{2x-5}{2\left ( 4x^{2}-9 \right )}-\frac{1}{x\left ( 2x+3 \right )}=0 \end{equation}
ОДЗ: \begin{equation}2x-3\neq 0 \end{equation} \begin{equation}2x\neq 3 \end{equation} \begin{equation}x\neq 1,5 \end{equation} \begin{equation}2x+3\neq 0 \end{equation} \begin{equation}2x\neq -3 \end{equation} \begin{equation}x\neq -1,5 \end{equation}
x(2x + 3) - x(2x - 5) - 2(2x - 3) = 0
2x² + 3x - 2x² + 5x - 4x + 6 = 0
4x + 6 = 0
4x = -6 \begin{equation}x=\frac{-6}{4} \end{equation}
x = -1,5
Ответ: решений нет
2)\begin{equation}\frac{3x-1}{6x-3}-\frac{1}{1-4x^{2}}=\frac{x}{2x+1} \end{equation} \begin{equation}\frac{3x-1}{3\left ( 2x-1 \right )}-\frac{1}{1-4x^{2}}-\frac{x}{2x+1}=0 \end{equation} \begin{equation}\frac{3x-1}{3\left ( 2x-1 \right )}+\frac{1}{4x^{2}-1}-\frac{x}{2x+1}=0 \end{equation}
ОДЗ: \begin{equation}2x-1\neq 0 \end{equation} \begin{equation}2x\neq 1 \end{equation} \begin{equation}x\neq 0,5 \end{equation} \begin{equation}2x+1\neq 0 \end{equation} \begin{equation}2x\neq -1 \end{equation} \begin{equation}x\neq -0,5 \end{equation}
(2x + 1)(3x - 1) + 3 - 3x(2x - 1) = 0
6x² - 2x + 3x - 1 + 3 - 6x² + 3x = 0
4x + 2 = 0
4x = -2 \begin{equation}x=\frac{-2}{4} \end{equation}
x = -0,5
Ответ: решений нет
3)\begin{equation}\frac{2x-2}{x²-36}-\frac{x-2}{x^{2}-6x}+\frac{x-1}{x^{2}+6x}=0 \end{equation} \begin{equation}\frac{2x-2}{x^{2}-36}-\frac{x-2}{x\left ( x-6 \right )}+\frac{x-1}{x\left ( x+6 \right )}=0 \end{equation}
ОДЗ: \begin{equation}x\neq 0 \end{equation} \begin{equation}x-6\neq 0 \end{equation} \begin{equation}x\neq 6 \end{equation} \begin{equation}x+6\neq 0 \end{equation} \begin{equation}x\neq -6 \end{equation}
x(2x - 2) - (x - 2)(x + 6) + (x - 1)(x - 6) = 0
2x² - 2x - (x² + 6x - 2x - 12) + x² - 6x - x + 6 = 0
2x² - 2x - x² - 4x + 12 - x² - 7x + 6 = 0
-13x + 18 = 0
-13x = -18 \begin{equation}x=\frac{-18}{-13} \end{equation} \begin{equation}x=\frac{18}{13}=1\frac{5}{13} \end{equation}
Ответ:\begin{equation}x=1\frac{5}{13} \end{equation}
4)\begin{equation}\frac{x+6}{x^{2}-7x}-\frac{4}{\left ( 7-x \right )^{2}}=\frac{1}{x-7} \end{equation} \begin{equation}\frac{x+6}{x\left ( x-7 \right )}-\frac{4}{\left ( x-7 \right )^{2}}-\frac{1}{x-7}=0 \end{equation}
ОДЗ: \begin{equation}x\neq 0 \end{equation} \begin{equation}x-7\neq 0 \end{equation} \begin{equation}x\neq 7 \end{equation}
(x - 7)(x + 6) - 4x - x(x - 7) = 0
x² + 6x - 7x - 42 - 4x - x² + 7x = 0
2x - 42 = 0
2x = 42
x = 21
Ответ: x = 21
5)\begin{equation}\frac{y+5}{y^{2}-5y}-\frac{y-5}{2y^{2}+10y}=\frac{y+25}{2y^{2}-50} \end{equation} \begin{equation}\frac{y+5}{y\left ( y-5 \right )}-\frac{y-5}{2y\left ( y+5 \right )}-\frac{y+25}{2\left ( y^{2}-25 \right )}=0 \end{equation}
ОДЗ: \begin{equation}y\neq 0 \end{equation} \begin{equation}y-5\neq 0 \end{equation} \begin{equation}y\neq 5 \end{equation} \begin{equation}y+5\neq 0 \end{equation} \begin{equation}y\neq -5 \end{equation}
2 · (y + 5)² - (y - 5)² - y(y + 25) = 0
2 · (y² + 10y + 25) - y² + 10y - 25 - y² - 25y = 0
2y² + 20y + 50 - y² + 10y - 25 - y² - 25y = 0
5y + 25 = 0
5y = -25
y = -5
Ответ: решений нет
6)\begin{equation}\frac{4\left ( y+9 \right )}{5y^{2}-45}+\frac{y+3}{5y^{2}-15y}=\frac{y-3}{y^{2}+3y} \end{equation} \begin{equation}\frac{4\left ( y+9 \right )}{5\left ( y^{2}-9 \right )}+\frac{y+3}{5y\left ( y-3 \right )}-\frac{y-3}{y\left ( y+3 \right )}=0 \end{equation}
ОДЗ: \begin{equation}y\neq 0 \end{equation} \begin{equation}y-3\neq 0 \end{equation} \begin{equation}y\neq 3 \end{equation} \begin{equation}y+3\neq 0 \end{equation} \begin{equation}y\neq -3 \end{equation}
4y(y + 9) + (y + 3)² - 5(y - 3)² = 0
4y² + 36y + y² + 6y + 9 - 5(y² - 6y + 9) = 0
4y² + y² + 42y + 9 - 5y² + 30y - 45 = 0
72y - 36 = 0
72y = 36 \begin{equation}y=\frac{36}{72} \end{equation} \begin{equation}y=\frac{1}{2} \end{equation}
Ответ: y = 0,5