Упростить: y = ((x^2-x-6) (x^2-x-2)) / x^2-4

1. Найдем корни квадратных трехчленов и разложим их на множители:

a) f (x) = x^2 - x - 6;

D = 1^2 + 4 * 6 = 25;

x = (1 ± √25) / 2 = (1 ± 5) / 2; x1 = (1 - 5) / 2 = - 4/2 = - 2; x2 = (1 + 5) / 2 = 6/2 = 3;

f (x) = (x + 2) (x - 3);

b) g (x) = x^2 - x - 2;

D = 1^2 + 4 * 2 = 9;

x = (1 ± √9) / 2 = (1 ± 3) / 2; x1 = (1 - 3) / 2 = - 2/2 = - 1; x2 = (1 + 3) / 2 = 4/2 = 2;

g (x) = (x + 1) (x - 2).

2. Сократим дробь:

y = (x^2 - x - 6) (x^2 - x - 2) / (x^2 - 4); y = (x + 2) (x - 3) (x + 1) (x - 2) / ((x + 2) (x - 2)); y = (x - 3) (x + 1).

Ответ: y = (x - 3) (x + 1).