$\frac{2x - 13}{x - 6} = \frac{x + 6}{x}$
x − 6 ≠ 0
x ≠ 6
и
x ≠ 0
$\frac{2x - 13}{x - 6} - \frac{x + 6}{x} = 0$ | * x(x − 6)
$x(2x - 13) - (x + 6)(x - 6) = 0$
$2x^2 - 13x - (x^2 - 36) = 0$
$2x^2 - 13x - x^2 + 36 = 0$
$x^2 - 13x + 36 = 0$
$D = b^2 - 4ac = (-13)^2 - 4 * 1 * 36 = 169 - 144 = 25 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{13 + \sqrt{25}}{2 * 1} = \frac{13 + 5}{2} = \frac{18}{2} = 9$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{13 - \sqrt{25}}{2 * 1} = \frac{13 - 5}{2} = \frac{8}{2} = 4$
Ответ: 4 и 9

$\frac{3x^2 - 4x - 20}{x + 2} = 2x - 5$
x + 2 ≠ 0
x ≠ −2
$\frac{3x^2 - 4x - 20}{x + 2} - (2x - 5) = 0$ | * (x + 2)
$3x^2 - 4x - 20 - (2x - 5)(x + 2) = 0$
$3x^2 - 4x - 20 - (2x^2 - 5x + 4x - 10) = 0$
$3x^2 - 4x - 20 - 2x^2 + x + 10 = 0$
$x^2 - 3x - 10 = 0$
$D = b^2 - 4ac = (-3)^2 - 4 * 1 * (-10) = 9 + 40 = 49 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{3 + \sqrt{49}}{2 * 1} = \frac{3 + 7}{2} = \frac{10}{2} = 5$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{3 - \sqrt{49}}{2 * 1} = \frac{3 - 7}{2} = \frac{-4}{2} = -2$ − не удовлетворяет условию, так как x ≠ −2.
Ответ: 5