How do you multiply \frac { x ^ { 2} - 4} { 12x } \cdot \frac { 3x } { x + 2}?

1 Answer
Nov 21, 2016

(x - 2)/4

Explanation:

First we should factor the quadratic x^2 - 4 or:

x^2 + 0x - 4 => (x - 2)(x + 2)

We can now multiply the numerator and denominator of the fractions:

((x - 2) * (x + 2) * 3x)/(12x * (x + 2))

We can regroup to:

((x - 2)*(x + 2)*3x)/((x + 2)*12x) =>

((x - 2)*(x + 2)*3x)/((x + 2)*4*3x) =>

((x - 2)*cancel((x + 2))*cancel(3x))/(cancel((x + 2))*4*cancel(3x)) =>

(x - 2)/4