SOLUTION: Simplify x^2+x-2/x^2-1

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Question 169795: Simplify
x^2+x-2/x^2-1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28x%5E2%2Bx-2%29%2F%28x%5E2-1%29 Start with the given expression.


%28%28x%2B2%29%28x-1%29%29%2F%28x%5E2-1%29 Factor x%5E2%2Bx-2 to get %28x%2B2%29%28x-1%29.


%28%28x%2B2%29%28x-1%29%29%2F%28%28x-1%29%28x%2B1%29%29 Factor x%5E2-1 to get %28x-1%29%28x%2B1%29.


%28%28x%2B2%29highlight%28%28x-1%29%29%29%2F%28highlight%28%28x-1%29%29%28x%2B1%29%29 Highlight the common terms.


%28%28x%2B2%29cross%28%28x-1%29%29%29%2F%28cross%28%28x-1%29%29%28x%2B1%29%29 Cancel out the common terms.


%28x%2B2%29%2F%28x%2B1%29 Simplify.


So %28x%5E2%2Bx-2%29%2F%28x%5E2-1%29 simplifies to %28x%2B2%29%2F%28x%2B1%29.


In other words, %28x%5E2%2Bx-2%29%2F%28x%5E2-1%29=%28x%2B2%29%2F%28x%2B1%29 where x%3C%3E-1 or x%3C%3E1