SOLUTION: x-4-[7/(x+2)] Divided by x+5+[2/(x+2)]

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Question 174861: x-4-[7/(x+2)] Divided by x+5+[2/(x+2)]
Answer by jim_thompson5910(28717) About Me  (Show Source):
You can put this solution on YOUR website!

%28x-4-7%2F%28x%2B2%29%29%2F%28x%2B5%2B2%2F%28x%2B2%29%29 Start with the given expression.


Multiply every term by the inner LCD x%2B2 to clear the inner fractions.


%28x%28x%2B2%29-4%28x%2B2%29-7%29%2F%28x%28x%2B2%29%2B5%28x%2B2%29%2B2%29 Simplify


%28x%5E2%2B2x-4x-8-7%29%2F%28x%5E2%2B2x%2B5x%2B10%2B2%29 Distribute


%28x%5E2-2x-15%29%2F%28x%5E2%2B7x%2B12%29 Combine like terms.


%28%28x-5%29%28x%2B3%29%29%2F%28x%5E2%2B7x%2B12%29 Factor the numerator


%28%28x-5%29%28x%2B3%29%29%2F%28%28x%2B4%29%28x%2B3%29%29 Factor the denominator


%28%28x-5%29highlight%28%28x%2B3%29%29%29%2F%28%28x%2B4%29highlight%28%28x%2B3%29%29%29 Highlight the common terms.


%28%28x-5%29cross%28%28x%2B3%29%29%29%2F%28%28x%2B4%29cross%28%28x%2B3%29%29%29 Cancel out the common terms.


%28x-5%29%2F%28x%2B4%29 Simplify


So %28x-4-7%2F%28x%2B2%29%29%2F%28x%2B5%2B2%2F%28x%2B2%29%29 simplifies to %28x-5%29%2F%28x%2B4%29