1. Find (2x+Sqrtxy+3y)/(x+sqrtxy-y) if (sqrtx)(sqrtx+sqrty)=3sqrty(sqrtx+5sqrty)
not sure how much you want to play with this, but if
√x(√x+√y) = 3√y(√x+5√y)
x + √xy = 3√xy + 15y
2√xy = x - 15y
Then on the left you have
2x + √xy + 3y
-------------------
x + √xy - y
and after making the substitution for √xy, that is
= (5x-9y) / (3x-17y)