$\frac{x^2 - 2x - 8}{x - 4}$
x − 4 ≠ 0
x ≠ 4
$x^2 - 2x - 8 = 0$
$D = b^2 - 4ac = (-2)^2 - 4 * 1 * (-8) = 4 + 32 = 36 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{2 + \sqrt{36}}{2 * 1} = \frac{2 + 6}{2} = \frac{8}{2} = 4$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{2 - \sqrt{36}}{2 * 1} = \frac{2 - 6}{2} = \frac{-4}{2} = -2$
$x^2 - 2x - 8 = (x - 4)(x - (-2)) = (x - 4)(x + 2)$
тогда:
$\frac{(x - 4)(x + 2)}{x - 4} = x + 2$
y = x + 2 при x ≠ 4

$\frac{x^2 - x - 2}{x + 1} - \frac{x^2 - x - 30}{x + 5}$
x + 1 ≠ 0
x ≠ −1
и
x + 5 ≠ 0
x ≠ −5
$x^2 - x - 2 = 0$
$D = b^2 - 4ac = (-1)^2 - 4 * 1 * (-2) = 1 + 8 = 9 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{1 + \sqrt{9}}{2 * 1} = \frac{1 + 3}{2} = \frac{4}{2} = 2$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{1 - \sqrt{9}}{2 * 1} = \frac{1 - 3}{2} = \frac{-2}{2} = -1$
$x^2 - 2x - 8 = (x - 2)(x - (-1)) = (x - 2)(x + 1)$

$x^2 - x - 30 = 0$
$D = b^2 - 4ac = (-1)^2 - 4 * 1 * (-30) = 1 + 120 = 121 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{1 + \sqrt{121}}{2 * 1} = \frac{1 + 11}{2} = \frac{12}{2} = 6$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{1 - \sqrt{121}}{2 * 1} = \frac{1 - 11}{2} = \frac{-10}{2} = -5$
$x^2 - x - 30 = (x - 6)(x - (-5)) = (x - 6)(x + 5)$
тогда:
$\frac{(x - 2)(x + 1)}{x + 1} - \frac{(x - 6)(x + 5)}{x + 5} = x - 2 - (x - 6) = x - 2 - x + 6 = 4$
y = 4 при x ≠ −5 и x ≠ −1