SOLUTION: i need help with this problem x^2-81/x^2-x-20 / x^2-8x-9/x^2+8x+16

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Question 325492: i need help with this problem x^2-81/x^2-x-20 / x^2-8x-9/x^2+8x+16
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%28x%5E2-81%29%2F%28x%5E2-x-20%29%29%2F%28%28x%5E2-8x-9%29%2F%28x%5E2%2B8x%2B16%29%29 Start with the given expression.


%28%28x%5E2-81%29%2F%28x%5E2-x-20%29%29%28%28x%5E2%2B8x%2B16%29%2F%28x%5E2-8x-9%29%29 Multiply the first fraction %28x%5E2-81%29%2F%28x%5E2-x-20%29 by the reciprocal of the second fraction %28x%5E2-8x-9%29%2F%28x%5E2%2B8x%2B16%29.


Factor x%5E2-81 to get %28x-9%29%2A%28x%2B9%29.


Factor x%5E2-x-20 to get %28x%2B4%29%2A%28x-5%29.


Factor x%5E2%2B8x%2B16 to get %28x%2B4%29%28x%2B4%29.


Factor x%5E2-8x-9 to get %28x%2B1%29%2A%28x-9%29.


Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


%28%28x%2B9%29%28x%2B4%29%29%2F%28%28x-5%29%28x%2B1%29%29 Simplify.


%28x%5E2%2B13x%2B36%29%2F%28x%5E2-4x-5%29 FOIL.


So %28%28x%5E2-81%29%2F%28x%5E2-x-20%29%29%2F%28%28x%5E2-8x-9%29%2F%28x%5E2%2B8x%2B16%29%29 simplifies to %28x%5E2%2B13x%2B36%29%2F%28x%5E2-4x-5%29.


In other words,