SOLUTION: x2+xy all over x2-y2

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Question 1197271: x2+xy all over x2-y2
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
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x2+xy all over x2-y2
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   %28x%5E2%2Bxy%29%2F%28x%5E2-y%5E2%29.


Factor the numerator    x%5E2%2Bxy%29 = x*(x+y).

Factor the denominator  x%5E2-y%5E2%29 =(x+y)*(x-y).


Therefore

    %28x%5E2%2Bxy%29%2F%28x%5E2-y%5E2%29 = %28x%2A%28x%2By%29%29%2F%28%28x%2By%29%2A%28x-y%29%29.


Cancel common factors (x+y) in the numerator and denominator

    %28x%5E2%2Bxy%29%2F%28x%5E2-y%5E2%29 = %28x%2A%28x%2By%29%29%2F%28%28x%2By%29%2A%28x-y%29%29 = x%2F%28x-y%29.


ANSWER.  %28x%5E2%2Bxy%29%2F%28x%5E2-y%5E2%29 = x%2F%28x-y%29, as algebraic expressions.

Solved and explained, with full step by step explanations.