Question

Simplify quantity 12 x minus 96 over quantity x squared minus 4x minus 32 all over quantity 6 x squared minus 6 x minus 12 over 3 x plus 4

Answer 1

First we will factorize polynomials:
x² - 4 x - 32 = x² - 8 x + 4 x - 32 = x ( x- 8 ) +4 ( x - 8 )= ( x - 8 ) ( x + 4 )
6(x² - x - 2 )= 6(x² - 2 x + x - 2) = 6(x ( x - 2 )+ ( x - 2 ))= 6 ( x - 2 ) ( x + 1 )
 $\frac{12(x-8)}{(x+4)(x-8)} : \frac{6(x-2)(x+1)}{3(x+1)} = \\ = \frac{12(x-8)}{(x+4)(x-8)}* \frac{3(x+1)}{6(x-2)(x+1)} = \\ \frac{6}{(x-2)(x+4)}$

Answer 2

((12x-96)/(x²-4x-32)) / ((6x²-6x-12)/(3x+3)) 
(12(x-8)/((x-8)(x+4)) * (3(x+1)/(6(x²-x-2))) 
(12/(x+4)) * ((x+1)/(2(x-2)(x+1))) 
(6/(x+4)) * (1/(x-2)) 
6/((x+4)(x-2)) 

6 / (x²+2x-8)