$\frac{5}{x} = 2 - \frac{3}{x - 2}$
$\frac{5}{x} + \frac{3}{x - 2} = 2$ |*x(x − 2)
$\begin{equation*} \begin{cases} 5(x - 2) + 3x = 2x(x - 2) &\\ x ≠ {0;2} & \end{cases} \end{equation*}$
$5x - 10 + 3x = 2x^2 - 4x$
$2x^2 - 12x + 10 = 0$
$x^2 - 6x + 5 = 0$
(x − 1)(x − 5) = 0
$\begin{equation*} \begin{cases} x_1 = 1; x_2 = 5 &\\ x ≠ {0;2} & \end{cases} \end{equation*}$
$x_1 = 1$;
$x_2 = 5$.

$\frac{3}{2x - 1} = 5x - 9$ |*(2x − 1)
$\begin{equation*} \begin{cases} 3 = (5x - 9)(2x - 1) &\\ x ≠ \frac{1}{2} & \end{cases} \end{equation*}$
$3 = 10x^2 - 23x + 9$
$10x^2 - 23x + 6 = 0$
$D = 23^2 - 4 * 10 * 6 = 289 = 17^2$
$x = \frac{23 ± 17}{20}$
$\begin{equation*} \begin{cases} x_1 = 0,3; x_2 = 2 &\\ x ≠ \frac{1}{2} & \end{cases} \end{equation*}$
$x_1 = 0,3$;
$x_2 = 2$.