document.write( "Question 1092635: Multiply and simplify show all work
\n" ); document.write( "X-8/(x+4)^2 × x^2-4x-32/(x-8)^2 \n" ); document.write( "

Algebra.Com's Answer #707300 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "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.

\n" ); document.write( " $\"%28%28x-8%29%2F%28x%2B4%29%5E2%29%2A%28%28x%5E2-4x-32%29%2F%28x-8%29%5E2%29\"$

\n" ); document.write( "You probably want to factor the quadratic expression first...
\n" ); document.write( " $\"%28%28x-8%29%2F%28x%2B4%29%5E2%29%2A%28%28x-8%29%28x%2B4%29%2F%28x-8%29%5E2%29\"$

\n" ); document.write( "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.

\n" ); document.write( "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.
\n" ); document.write( " $\"1%2F%28x%2B4%29\"$
\n" ); document.write( " \n" ); document.write( "

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