$\frac{24}{x - 2} + \frac{16}{x + 2} = 3$
x − 2 ≠ 0
x ≠ 2
и
x + 2 ≠ 0
x ≠ −2
$\frac{24}{x - 2} + \frac{16}{x + 2} = 3$ | * (x − 2)(x + 2)
$24(x + 2) + 16(x - 2) = 3(x^2 - 4)$
$24x + 48 + 16x - 32 = 3x^2 - 12$
$-3x^2 + 40x + 16 + 12 = 0$
$-3x^2 + 40x + 28 = 0$
$D = b^2 - 4ac = 40^2 - 4 * (-3) * 28 = 1600 + 336 = 1936 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-40 + \sqrt{1936}}{2 * (-3)} = \frac{-40 + 44}{-6} = \frac{4}{-6} = -\frac{2}{3}$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-40 - \sqrt{1936}}{2 * (-3)} = \frac{-40 - 44}{-6} = \frac{-84}{-6} = 14$ − не удовлетворяет условию, так как x ≠ 10.
Ответ: при $x = -\frac{2}{3}$ и x = 14

$\frac{42}{x} - \frac{36}{x + 20} = \frac{1}{4}$
x ≠ 0
и
x + 20 ≠ 0
x ≠ −20
$\frac{42}{x} - \frac{36}{x + 20} = \frac{1}{4}$ | * 4x(x + 20)
42 * 4(x + 20) − 36 * 4x = x(x + 20)
$168x + 3360 - 144x = x^2 + 20x$
$-x^2 + 24x + 3360 - 20x = 0$
$-x^2 + 4x + 3360 = 0$ | * (−1)
$x^2 - 4x - 3360 = 0$
$D = b^2 - 4ac = (-4)^2 - 4 * 1 * (-3360) = 16 + 13440 = 13456 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{4 + \sqrt{13456}}{2 * 1} = \frac{4 + 116}{2} = \frac{120}{2} = 60$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{4 - \sqrt{13456}}{2 * 1} = \frac{4 - 116}{2} = \frac{-112}{2} = -56$
Ответ: при x = −56 и x = 60