$\frac{8x^2 - 3}{5} - \frac{5 - 9x^2}{4} = 2$ |*20
$4(8x^2 - 3) - 5(5 - 9x^2) = 40$
$32x^2 - 12 - 25 + 45x^2 - 40 = 0$
$77x^2 = 77$
$x^2 = 1$
x = ±1

$\frac{2}{x^2 - x + 1} - \frac{1}{x + 1} = \frac{2x - 1}{x^3 + 1}$
$\begin{equation*} \begin{cases} 2(x + 1) - (x^2 - x + 1) = 2x - 1 &\\ x ≠ 1 & \end{cases} \end{equation*}$
$2(x + 1) - (x^2 - x + 1) = 2x - 1$
$2x + 2 - x^2 + x - 1 - 2x + 1 = 0$
$-x^2 + x + 2 = 0$
$x^2 - x - 2 = 0$
(x − 2)(x + 1) = 0
x − 2 = 0
x = 2
x + 1 = 0
x = −1
$\begin{equation*} \begin{cases} x_1 = -1; x_2 = 2 &\\ x ≠ 1 & \end{cases} \end{equation*}$
x = 2

$\frac{10}{x^2 - 4} - \frac{3}{2x - 4} = \frac{1}{2}$ |*2(x − 2)(x + 2)
$\begin{equation*} \begin{cases} 20 - 3(x + 2) = (x - 2)(x + 2) &\\ x ≠ ±2 & \end{cases} \end{equation*}$
$20 - 3x - 6 = x^2 - 4$
$x^2 + 3x - 18 = 0$
(x + 6)(x − 3) = 0
$\begin{equation*} \begin{cases} x_1 = -6; x_2 = 3 &\\ x ≠ ±2 & \end{cases} \end{equation*}$
$x_1 = -6$;
$x_2 = 3$.

$x - \frac{x^2 - 17}{x - 3} = \frac{5}{x}$ |x(x − 3)
$\begin{equation*} \begin{cases} x^2(x - 3) - x(x^2 - 17) = 5(x - 3) &\\ x ≠ {0; 3} & \end{cases} \end{equation*}$
$x^3 - 3x^2 - x^3 + 17x = 5x - 15$
$-3x^2 + 12x + 15 = 0$
$x^2 - 4x - 5 = 0$
(x + 1)(x − 5) = 0
$\begin{equation*} \begin{cases} x_1 = -1; x_2 = 5 &\\ x ≠ {0; 3} & \end{cases} \end{equation*}$
$x_1 = -1$;
$x_2 = 5$.