SOLUTION: Simplify x2+5x+6 x2-5x+6 --------x-------- x2-4 x2-9

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Question 118911: Simplify

x2+5x+6 x2-5x+6
--------x--------
x2-4 x2-9
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%28x%5E2%2B5x%2B6%29%2F%28x%5E2-4%29%29%28%28x%5E2-5x%2B6%29%2F%28x%5E2-9%29%29 Start with the given expression

%28%28%28x%2B3%29%28x%2B2%29%29%2F%28x%5E2-4%29%29%28%28x%5E2-5x%2B6%29%2F%28x%5E2-9%29%29 Factor x%5E2%2B5x%2B6 to get %28x%2B3%29%28x%2B2%29

Factor x%5E2-4 to get %28x%2B2%29%28x-2%29

Factor x%5E2-5x%2B6 to get %28x-3%29%28x-2%29

Factor x%5E2-9 to get %28x%2B3%29%28x-3%29


%28x%2B3%29%28x%2B2%29%28x-3%29%28x-2%29%2F%28x%2B2%29%28x-2%29%28x%2B3%29%28x-3%29 Combine the fractions


Cancel like terms


1 Simplify


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Answer:

So %28%28x%5E2%2B5x%2B6%29%2F%28x%5E2-4%29%29%28%28x%5E2-5x%2B6%29%2F%28x%5E2-9%29%29 simplifies to 1. In other words %28%28x%5E2%2B5x%2B6%29%2F%28x%5E2-4%29%29%28%28x%5E2-5x%2B6%29%2F%28x%5E2-9%29%29=1