SOLUTION: whats the multiplicative inverse of {{{(x^2+y^2)/(x-y)}}}

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Question 185954: whats the multiplicative inverse of %28x%5E2%2By%5E2%29%2F%28x-y%29
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
whats the multiplicative inverse of %28x%5E2%2By%5E2%29%2F%28x-y%29
That asks the question:
What do you have to multiply %28x%5E2%2By%5E2%29%2F%28x-y%29 by to get 1?
Answer: You have to multiply it by the reciprocal of itself
in order to get 1. So the answer is its reciprocal, namely,
%28x-y%29%2F%28x%5E2%2By%5E2%29
To show why that's the answer, we multiply the original by it
%28%28x%5E2%2By%5E2%29%2F%28x-y%29%29%28%28x-y%29%2F%28x%5E2%2By%5E2%29%29
Then we cancel:


and that just gives 1
Edwin