SOLUTION: simplify x^2+2xy+y^2/x+y * x^2-y^2/x-y

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Question 169797: simplify
x^2+2xy+y^2/x+y * x^2-y^2/x-y
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%28x%5E2%2B2xy%2By%5E2%29%2F%28x%2By%29%29%28%28x%5E2-y%5E2%29%2F%28x-y%29%29 Start with the given expression.


%28%28%28x%2By%29%28x%2By%29%29%2F%28x%2By%29%29%28%28x%5E2-y%5E2%29%2F%28x-y%29%29 Factor x%5E2%2B2xy%2By%5E2 to get %28x%2By%29%28x%2By%29.


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


%28%28x%2By%29%28x%2By%29%28x-y%29%28x%2By%29%29%2F%28%28x%2By%29%28x-y%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


%28x%2By%29%28x%2By%29 Simplify.


%28x%2By%29%5E2 Condense the expression


So %28%28x%5E2%2B2xy%2By%5E2%29%2F%28x%2By%29%29%28%28x%5E2-y%5E2%29%2F%28x-y%29%29 simplifies to %28x%2By%29%5E2.


In other words, where x%3C%3Ey or x%3C%3E-y