Найдите корни уравнения 1/х (в квадрате) - 6 х+8 - 1/х-2 + 10/х (в квадрате) - 4=0

1 / (х² - 6 х + 8) - 1 / (х - 2) + 10 / (х² - 4) = 0;

х² - 6 х + 8 = 0;

D = 36 - 4 * 1 * 8 = 36 - 32 = 4 > 0;

x₁ = (6 - 2) / 2 = 4/2 = 2;

x₂ = (6 + 2) / 2 = 8/2 = 4.

х² - 6 х + 8 = (x - 2) (x - 4).

1 / (x - 2) (x - 4) - 1 / (х - 2) + 10 / (х - 2) (x + 2) = 0;

(1 * (x + 2) - 1 * (x + 2) (x - 4) + 10 * (x - 4)) / (x + 2) (x - 2) (x - 4) = 0;

ОДЗ: x ≠ - 2, x ≠ 2, x ≠ 4.

x + 2 - (x² - 4x + 2x - 8) + 10x - 40 = 0;

x + 2 - x² + 4x - 2x + 8 + 10x - 40 = 0;

- x² + 13x - 30 = 0;

x² - 13x + 30 = 0;

D = 169 - 4 * 1 * 30 = 169 - 120 = 49 > 0;

x₁ = (13 - 7) / 2 = 6/2 = 3;

x₂ = 20/2 = 10.

Ответ: x = 3; x = 10.