SOLUTION: simplify and give restrictions x squared - y squared ___________ _________ x squared + 3xy + 2y squared

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Question 184586: simplify and give restrictions
x squared - y squared
_____________________
x squared + 3xy + 2y squared
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28x%5E2-y%5E2%29%2F%28x%5E2%2B3xy%2B2y%5E2%29 Start with the given expression.


%28%28x-y%29%2A%28x%2By%29%29%2F%28x%5E2%2B3xy%2B2y%5E2%29 Factor x%5E2-y%5E2 to get %28x-y%29%2A%28x%2By%29.


%28%28x-y%29%2A%28x%2By%29%29%2F%28%28x%2B2y%29%28x%2By%29%29 Factor x%5E2%2B3xy%2B2y%5E2 to get %28x%2B2y%29%28x%2By%29.


%28%28x-y%29highlight%28%28x%2By%29%29%29%2F%28%28x%2B2y%29highlight%28%28x%2By%29%29%29 Highlight the common terms.


%28%28x-y%29cross%28%28x%2By%29%29%29%2F%28%28x%2B2y%29cross%28%28x%2By%29%29%29 Cancel out the common terms.


%28x-y%29%2F%28x%2B2y%29 Simplify.


So %28x%5E2-y%5E2%29%2F%28x%5E2%2B3xy%2B2y%5E2%29 simplifies to %28x-y%29%2F%28x%2B2y%29.


In other words, %28x%5E2-y%5E2%29%2F%28x%5E2%2B3xy%2B2y%5E2%29=%28x-y%29%2F%28x%2B2y%29 where x%3C%3E-y or x%3C%3E-2y