SOLUTION: Divide the following fractions. 16x/4x^2-16 divided by 4x-24/x^2- 4x -12

Algebra ->  Expressions-with-variables -> SOLUTION: Divide the following fractions. 16x/4x^2-16 divided by 4x-24/x^2- 4x -12       Log On


   

Question 107084: Divide the following fractions.
16x/4x^2-16 divided by 4x-24/x^2- 4x -12
Answer by Annabelle1(69) About Me  (Show Source):
You can put this solution on YOUR website!
facrorise all components of this question first.
4x^2-16 =4(x^2-4)= 4(x-2)(x+2) (differnce of 2 squares)
4x-24=4(x-6)
x^2-4x-12= (x-6)(x+2)
when we divide two fractions, we can flip the second one up-side-down and multiply
so we have:
16x%2F%284%28x-2%29%28x%2B2%29%29 multiplied by %28%28x-6%29%28x%2B2%29%29%2F%284%28x-6%29%29
which is %2816x%28x-6%29%28x%2B2%29%29%2F%2816%28x-2%29%28x%2B2%29%28x-6%29%29
a lot of terms now cancel like the 16, x-6, x+2
we are left with x%2F%28x-2%29