x^2 + x - 12 factors as (x + 4) ( x - 3)
3x^2 + 11x - 4 factors as ( 3x - 1) (x + 4)
x^2 - 4 = (x + 2) (x - 2)
So we have
(x + 4) ( x - 3)
___________
(x - 2)
_______________ =
(3x - 1) ( x + 4)
____________
(x + 2) ( x - 2)
(x + 4) ( x - 3) (x + 2) ( x - 2)
____________ * ____________ =
(x - 2) (3x - 1) ( x + 4)
(x + 4) ( x - 3) ( x + 2) ( x - 2)
______________________ =
(x - 2) ( 3x - 1) ( x + 4)
(x - 3) ( x + 2)
___________ =
3x - 1
x^2 - x - 6
________
3x - 1