# How do you factor (7x^2+11x-6)/(x^2-4)?

Jul 21, 2016

$\frac{7 x - 3}{x - 2}$

#### Explanation:

First, factor the numerator y by the new AC Method (Socratic Search).
y = 7x^2 + 11x - 6 = 7(x + p)(x + q)
Converted trinomial y' = x^2 + 11x - 42 = (x + p')(x + q')
p' and q' have opposite signs. Factor pairs of (ac = -42) -->
(-2, 21(-3, 14). This last sum is (11 = b). Then p' = -3 and q' = 14.
Back to original trinomial y, $p = p \frac{'}{a} = - \frac{3}{7}$, and
$q = \frac{q '}{a} = \frac{14}{7} = 2.$
Factor form of y:
y = 7(x - 3/7)(x + 2) = (7x - 3)(x + 2) Factored form of f(x) = ((7x - 3)(x + 2))/((x - 2)(x + 2)) = f(x) = (7x - 3)/(x - 2)#