$\frac{2x - 5}{x + 5} - 4 = 0$
$\frac{2x - 5 - 4(x + 5)}{x + 5} = 0$
$\frac{-2x - 25}{x + 5} = 0$
$\begin{equation*} \begin{cases} -2x - 25 = 0 &\\ x + 5 ≠ 0 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x = -12,5 &\\ x ≠ -5 & \end{cases} \end{equation*}$
Ответ: x = −12,5

$\frac{12}{7 - x} = x$
$\frac{12}{7 - x} - x = 0$
$\frac{12 - x(7 - x)}{7 - x} = 0$
$\frac{x^2 - 7x + 12}{7 - x} = 0$
$\begin{equation*} \begin{cases} x^2 - 7x + 12 = 0 &\\ 7 - x ≠ 0 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} (x - 3)(x - 4) = 0 &\\ x ≠ 7 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x = {3;4} &\\ x ≠ 7 & \end{cases} \end{equation*}$
Ответ: x = {3;4}

$\frac{x^2 - 4}{4x} = \frac{3x - 2}{2x}$
$\frac{x^2 - 4}{4x} - \frac{3x - 2}{2x} = 0$
$\frac{x^2 - 4 - 2(3x - 2)}{4x} = 0$
$\frac{x^2 - 6x}{4x} = 0$
$\begin{equation*} \begin{cases} x^2 - 6x = 0 &\\ 4x ≠ 0 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x(x - 6) = 0 &\\ x ≠ 0 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x = {0;6} &\\ x ≠ 0 & \end{cases} \end{equation*}$
Ответ: x = 6

$\frac{10}{2x - 3} = x - 1$
$\frac{10}{2x - 3} - (x - 1) = 0$
$\frac{10 - (x - 1)(2x - 3)}{2x - 3} = 0$
$\frac{10 - (2x^2 - 5x + 3)}{2x - 3} = 0$
$\frac{-2x^2 + 5x + 7}{2x - 3} = 0$
$\begin{equation*} \begin{cases} -2x^2 + 5x + 7 = 0 &\\ 2x - 3 ≠ 0 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 2x^2 - 5x - 7 = 0 &\\ x ≠ 1,5 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} (2x - 7)(x + 1) = 0 &\\ x ≠ 1,5 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x = {-1;3,5} &\\ x ≠ 1,5 & \end{cases} \end{equation*}$
Ответ: x = {−1;3,5}

$\frac{8}{x} = 3x + 2$
$\frac{8}{x} - (3x + 2) = 0$
$\frac{8 - x(3x + 2)}{x} = 0$
$\frac{-3x^2 - 2x + 8}{x} = 0$
$\begin{equation*} \begin{cases} -3x^2 - 2x + 8 = 0 &\\ x ≠ 0 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 3x^2 + 2x - 8 = 0 &\\ x ≠ 0 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} (3x - 4)(x + 2) = 0 &\\ x ≠ 0 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x = {-2; 1\frac{1}{3}} &\\ x ≠ 0 & \end{cases} \end{equation*}$
Ответ: $x = {-2; 1\frac{1}{3}}$

$\frac{x^2 + 4x}{x + 2} = \frac{2x}{3}$
$\frac{x^2 + 4x}{x + 2} - \frac{2x}{3} = 0$
$\frac{3(x^2 + 4x) - 2x(x + 2)}{3(x + 2)} = 0$
$\frac{3x^2 + 12x - 2x^2 - 4x}{3(x + 2)} = 0$
$\frac{3x^2 + 12x - 2x^2 - 4x}{3(x + 2)} = 0$
$\frac{x^2 + 8x}{3(x + 2)} = 0$
$\begin{equation*} \begin{cases} x^2 + 8x = 0 &\\ 3(x + 2) ≠ 0 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x(x + 8) = 0 &\\ x ≠ -2 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x = {-8;0} &\\ x ≠ -2 & \end{cases} \end{equation*}$
Ответ: x = {−8;0}

$\frac{2x^2 - 5x + 3}{10x - 5} = 0$
$\begin{equation*} \begin{cases} 2x^2 - 5x + 3 = 0 &\\ 10x - 5 ≠ 0 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} (2x - 3)(x - 1) = 0 &\\ x ≠ -0,5 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x = {1;1,5} &\\ x ≠ 0,5 & \end{cases} \end{equation*}$
Ответ: x = {1;1,5}

$\frac{4x^2 - 9x}{x + 1,5} = 0$
$\begin{equation*} \begin{cases} 4x^3 - 9x = 0 &\\ x + 1,5 ≠ 0 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x(4x^2 - 9) = 0 &\\ x ≠ -1,5 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x(2x - 3)(2x + 3) = 0 &\\ x ≠ -1,5 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x = {0;±1,5} &\\ x ≠ -1,5 & \end{cases} \end{equation*}$
Ответ: x = {0;1,5}