SOLUTION: Rationalize the denominator: {{{(sqrt(x)-sqrt(y))/(sqrt(x)+sqrt(y))}}}

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Question 131897: Rationalize the denominator: %28sqrt%28x%29-sqrt%28y%29%29%2F%28sqrt%28x%29%2Bsqrt%28y%29%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%28x%29-sqrt%28y%29%29%2F%28sqrt%28x%29%2Bsqrt%28y%29%29 Start with the given expression


Multiply by the fraction by %28sqrt%28x%29-sqrt%28y%29%29%2F%28sqrt%28x%29-sqrt%28y%29%29. Note sqrt%28x%29-sqrt%28y%29 is the conjugate of sqrt%28x%29%2Bsqrt%28y%29.


Combine the fractions


Foil the denominator


Cancel like terms


%28%28sqrt%28x%29-sqrt%28y%29%29%28sqrt%28x%29-sqrt%28y%29%29%29%2F%28x-y%29 Multiply


%28sqrt%28x%29sqrt%28x%29-2sqrt%28x%29sqrt%28y%29%2Bsqrt%28y%29sqrt%28y%29%29%2F%28x-y%29 Foil the numerator


%28x-2sqrt%28x%29sqrt%28y%29%2By%29%2F%28x-y%29 Multiply



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Answer:
So %28sqrt%28x%29-sqrt%28y%29%29%2F%28sqrt%28x%29%2Bsqrt%28y%29%29 simplifies to %28x-2sqrt%28x%29sqrt%28y%29%2By%29%2F%28x-y%29