6 х2 + х - 2 дробь 3 х2 - 4 х - 4

(6 * х² + х - 2) / (3 * x² - 4 * x - 4);

Разложим многочлен на множители.

1) 6 * x² + x - 2 = 0;

D = b² - 4 * a * c = 1² - 4 * 6 * (-2) = 1 + 4 * 6 * 2 = 1 + 8 * 6 = 1 + 48 = 49 = 7²;

x1 = (-1 + 7) / (2 * 12) = 6/24 = 1/4;

x2 = (-1 - 7) / (2 * 12) = - 8/24 = - 1/3;

2) 3 * x² - 4 * x - 4 = 0;

D = (-4) ² - 4 * 3 * (-4) = 16 + 16 * 3 = 16 * 4 = 64 = 8²;

x1 = (4 + 8) / (2 * 3) = 12/6 = 2;

x2 = (4 - 8) / (2 * 3) = - 4/6 = - 2/3;

Отсюда получаем:

(6 * х² + х - 2) / (3 * x² - 4 * x - 4);

6 * (x - 1/4) * (x + 1/3) / (3 * (x - 2) * (x + 2/3)).