x2 - x - 12
First try and factor that expression.
Notice that it happens to be the product of (x - 4) and (x + 3). This makes your problem easy.
(x2 - x - 12) / (x - 4)
= (x - 4) (x + 3) / (x - 4)
Now just divide numerator and denominator by the common factor. ("Cancel" (x - 4) out of numerator and denominator.)
Wind up with the answer = (x + 3)
(x2-x-12)/(x-4) = (x+3)
14
x2 + x - 12 = (x + 4)(x - 3)
If: x2+x = 12 Then: x2+x-12 = 0 And using the quadratic formula: x = -4 or x = 3
4 x 2 + 4 = 12 x = 4
(x2-x-12)/(x-4) = (x+3)
14
x2 - x - 12 = 0 ∴ (x + 3)(x - 4) = 0 ∴ x ∈ {-3, 4}
x2 + x - 12 = (x + 4)(x - 3)
14
If: x2+x = 12 Then: x2+x-12 = 0 And using the quadratic formula: x = -4 or x = 3
If that's x2, the answer is (x - 5)(x - 4)
-10
4 x 2 + 4 = 12 x = 4
Divide all terms by 4:- x2+7x+12 = (x+3)(x+4) when factored
x2-7x+12 (x-3)(x-4)
(x2 - 4)/4x = 12; x ≠ 0 x2 - 4 = 48x x2 - 48x = 4 x2 - 48x + 242= 4 + 242 (x - 24)2 = 4 + 576 x - 24 = ±√580 x = 24 ± 2√145