SOLUTION: Simplify the rational expression: x2 + 3x – 10/ x2 + x – 20

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Question 167721: Simplify the rational expression:
x2 + 3x – 10/ x2 + x – 20
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28x%5E2%2B3x-10%29%2F%28x%5E2%2Bx-20%29 Start with the given expression.


%28%28x%2B5%29%28x-2%29%29%2F%28x%5E2%2Bx-20%29 Factor x%5E2%2B3x-10 to get %28x%2B5%29%28x-2%29.


%28%28x%2B5%29%28x-2%29%29%2F%28%28x%2B5%29%28x-4%29%29 Factor x%5E2%2Bx-20 to get %28x%2B5%29%28x-4%29.


%28highlight%28%28x%2B5%29%29%28x-2%29%29%2F%28highlight%28%28x%2B5%29%29%28x-4%29%29 Highlight the common terms.


%28cross%28%28x%2B5%29%29%28x-2%29%29%2F%28cross%28%28x%2B5%29%29%28x-4%29%29 Cancel out the common terms.


%28x-2%29%2F%28x-4%29 Simplify.


So %28x%5E2%2B3x-10%29%2F%28x%5E2%2Bx-20%29 simplifies to %28x-2%29%2F%28x-4%29.


In other words, %28x%5E2%2B3x-10%29%2F%28x%5E2%2Bx-20%29=%28x-2%29%2F%28x-4%29 where x%3C%3E-5 or x%3C%3E4