Question 88878
{{{sqrt(x)/ (3*sqrt(x) - sqrt(y))}}}


{{{(sqrt(x)/ (3*sqrt(x) - sqrt(y)))((3*sqrt(x) + sqrt(y))/(3*sqrt(x) + sqrt(y)))}}} Multiply the fraction by {{{((3*sqrt(x) + sqrt(y))/(3*sqrt(x) + sqrt(y)))}}}


{{{(sqrt(x)(3*sqrt(x) + sqrt(y))/ (3*sqrt(x) - sqrt(y))(3*sqrt(x) + sqrt(y)))}}}


{{{(sqrt(x)*3*sqrt(x) + sqrt(x)*sqrt(y))/ (3*sqrt(x) - sqrt(y))(3*sqrt(x) + sqrt(y)))}}} Distribute


{{{(3*x + sqrt(x)*sqrt(y))/ (9x-y)}}} Multiply


{{{(3x + sqrt(x)*sqrt(y))/( 3*sqrt(x)*3*sqrt(x)+3*sqrt(x)*sqrt(y)-3*sqrt(x)*sqrt(y)-sqrt(y)*sqrt(y))}}}FOIL the denominator



{{{(3x + sqrt(x)*sqrt(y))/ (9x-y)}}} Combine like terms


{{{(3x + sqrt(xy))/ (9x-y)}}} Combine the square roots






So the answer is {{{(3*x + sqrt(xy))/ (9x-y)}}}  note: this is just like your last choice, but it has 3x minus the square root instead of 3x plus the square root, so check your choices again.