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

Question 1092635: Multiply and simplify show all work
X-8/(x+4)^2 � x^2-4x-32/(x-8)^2
Answer by greenestamps(13200) (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.

You probably want to factor the quadratic expression first...

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.

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