SOLUTION: x - 2 over x - x over x + 3

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Question 153113: x - 2 over x - x over x + 3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28x-2%29%2F%28x%29-x%2F%28x%2B3%29 Start with the given expression.


%28%28x%2B3%29%2F%28x%2B3%29%29%28%28x-2%29%2F%28x%29%29-x%2F%28x%2B3%29 Multiply the 1st term %28x-2%29%2F%28x%29 by %28x%2B3%29%2F%28x%2B3%29


%28%28x-2%29%28x%2B3%29%29%2F%28x%28x%2B3%29%29-x%2F%28x%2B3%29 Combine the fractions.



%28x%5E2%2Bx-6%29%2F%28x%28x%2B3%29%29-x%2F%28x%2B3%29 FOIL


%28x%5E2%2Bx-6%29%2F%28x%28x%2B3%29%29-%28x%2Fx%29%28x%2F%28x%2B3%29%29 Multiply the 2nd term x%2F%28x%2B3%29 by x%2Fx



%28x%5E2%2Bx-6%29%2F%28x%28x%2B3%29%29-%28x%5E2%29%2F%28x%28x%2B3%29%29 Combine the fractions.


%28x%5E2%2Bx-6-x%5E2%29%2F%28x%28x%2B3%29%29 Subtract the fractions.


%28x-6%29%2F%28x%28x%2B3%29%29 Combine like terms


%28x-6%29%2F%28x%5E2%2B3x%29 Distribute


So %28x-2%29%2F%28x%29-x%2F%28x%2B3%29=%28x-6%29%2F%28x%5E2%2B3x%29 where x%3C%3E0 or x%3C%3E-3