SOLUTION: Multiply. State any restrictions on the variable x^2+6x-7/x^2+5x times 3x^2+16x+5/2x^2+7x-9

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Question 189464: Multiply. State any restrictions on the variable


x^2+6x-7/x^2+5x times 3x^2+16x+5/2x^2+7x-9
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x%5E2%2B6x-7%29%2F%28x%5E2%2B5x%29%29%28%283x%5E2%2B16x%2B5%29%2F%282x%5E2%2B7x-9%29%29 Start with the given expression


%28%28%28x%2B7%29%28x-1%29%29%2F%28x%5E2%2B5x%29%29%28%283x%5E2%2B16x%2B5%29%2F%282x%5E2%2B7x-9%29%29 Factor the first numerator


%28%28%28x%2B7%29%28x-1%29%29%2F%28x%28x%2B5%29%29%29%28%283x%5E2%2B16x%2B5%29%2F%282x%5E2%2B7x-9%29%29 Factor the first denominator


%28%28%28x%2B7%29%28x-1%29%29%2F%28x%28x%2B5%29%29%29%28%28%28x%2B5%29%283x%2B1%29%29%2F%282x%5E2%2B7x-9%29%29 Factor the second numerator


%28%28%28x%2B7%29%28x-1%29%29%2F%28x%28x%2B5%29%29%29%28%28%28x%2B5%29%283x%2B1%29%29%2F%28%282x%2B9%29%28x-1%29%29%29 Factor the second denominator


%28%28x%2B7%29%28x-1%29%28x%2B5%29%283x%2B1%29%29%2F%28x%28x%2B5%29%282x%2B9%29%28x-1%29%29 Combine the fractions.


%28%28x%2B7%29highlight%28%28x-1%29%29highlight%28%28x%2B5%29%29%283x%2B1%29%29%2F%28x%2Ahighlight%28%28x%2B5%29%29%282x%2B9%29highlight%28%28x-1%29%29%29 Highlight the common terms


%28%28x%2B7%29cross%28%28x-1%29%29cross%28%28x%2B5%29%29%283x%2B1%29%29%2F%28x%2Across%28%28x%2B5%29%29%282x%2B9%29cross%28%28x-1%29%29%29 Cancel out the common terms.


%28%28x%2B7%29%283x%2B1%29%29%2F%28x%282x%2B9%29%29 Simplify


%283x%5E2%2B22x%2B7%29%2F%28x%282x%2B9%29%29 FOIL


%283x%5E2%2B22x%2B7%29%2F%282x%5E2%2B9x%29 Distribute


So %28%28x%5E2%2B6x-7%29%2F%28x%5E2%2B5x%29%29%28%283x%5E2%2B16x%2B5%29%2F%282x%5E2%2B7x-9%29%29 simplifies to %283x%5E2%2B22x%2B7%29%2F%282x%5E2%2B9x%29


In other words, %28%28x%5E2%2B6x-7%29%2F%28x%5E2%2B5x%29%29%28%283x%5E2%2B16x%2B5%29%2F%282x%5E2%2B7x-9%29%29=%283x%5E2%2B22x%2B7%29%2F%282x%5E2%2B9x%29 where x%3C%3E-5, x%3C%3E-9%2F2, x%3C%3E0, or x%3C%3E1 (these are the restrictions)