SOLUTION: Multiply and simplify show all work X-8/(x+4)^2 × x^2-4x-32/(x-8)^2

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Question 1092635: Multiply and simplify show all work
X-8/(x+4)^2 × x^2-4x-32/(x-8)^2

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Since the problem says to multiply and simplify, I assume the product can be simplified. So I added parentheses to show what I THINK the expression is supposed to be.

%28%28x-8%29%2F%28x%2B4%29%5E2%29%2A%28%28x%5E2-4x-32%29%2F%28x-8%29%5E2%29

You probably want to factor the quadratic expression first...
%28%28x-8%29%2F%28x%2B4%29%5E2%29%2A%28%28x-8%29%28x%2B4%29%2F%28x-8%29%5E2%29

When you multiply fractions, the numerators get multiplied together and the denominators get multiplied together, so we can consider the expression in this form as a single fraction. Doing that, we see two factors of (x-8) in both numerator and denominator, so they all cancel. And the remaining factors are one factor of (x+4) in the numerator and two in the denominator; the one in the numerator cancels with one of the two in the denominator, leaving one factor of (x+4) in the denominator.

So the only binomial factor left is (x+4) in the denominator. But remember that when we cancel common factors, they don't disappear completely -- they leave a "1" behind. So the final answer has "1" in the numerator and one factor of (x+4) in the denominator.
1%2F%28x%2B4%29