Question

The answer is C, so please explain why and the process of getting there :)

Simplify: (6x^(2)-8)/(x-3y)* (36y^(2)-4x^(2))/(9x^(2)-12)

A. 8(x^2-3y)/2
B. x^2-6xy/3x
C. -8(3y+x)/3
D. 8(x-3y)

Answer 1

To simplify the given expression, factor and cancel out common terms to get the final simplified expression as -8(3y + x) / 3.

Step-by-step explanation:

To simplify the expression, we need to factor and cancel out common terms. Let's break down the steps:

1. Factor the numerators and denominators:
   (6x^2 - 8) = 2(3x^2 - 4)
   (36y^2 - 4x^2) = 4(9y^2 - x^2)
   (9x^2 - 12) = 3(3x^2 - 4)
2. Cancel out common terms:
   2 and 4 cancel out
   (3x^2 - 4) and (3x^2 - 4) cancel out
3. The final simplified expression is:
   -8(3y + x) / 3