Question 1092635
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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.<br>
{{{((x-8)/(x+4)^2)*((x^2-4x-32)/(x-8)^2)}}}<br>
You probably want to factor the quadratic expression first...
{{{((x-8)/(x+4)^2)*((x-8)(x+4)/(x-8)^2)}}}<br>
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.<br>
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/(x+4)}}}