Question 199880
{{{(sqrt(x))/(sqrt(x)-sqrt(y))}}} Start with the given expression.



{{{(sqrt(x)(sqrt(x)+sqrt(y)))/((sqrt(x)-sqrt(y))(sqrt(x)+sqrt(y)))}}} Multiply both the numerator and denominator by {{{sqrt(x)+sqrt(y)}}}



{{{(sqrt(x)(sqrt(x)+sqrt(y)))/((sqrt(x))^2-(sqrt(y))^2)}}} FOIL



{{{(sqrt(x)(sqrt(x)+sqrt(y)))/(x-y)}}} Square the square roots.



{{{(sqrt(x)*sqrt(x)+sqrt(x)*sqrt(y))/(x-y)}}} Distribute



{{{(sqrt(x^2)+sqrt(xy))/(x-y)}}} Combine the roots.



{{{(x+sqrt(xy))/(x-y)}}} Take the square root of {{{x^2}}} to get "x"



So {{{(sqrt(x))/(sqrt(x)-sqrt(y))=(x+sqrt(xy))/(x-y)}}} where {{{x>0}}}, {{{y>0}}}, and {{{x<>y}}}



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