Question

(a*sqrt(a)+b*sqrt(b))/(a-sqrt(ab)+b)

Answer 1

$sqrt{b} + sqrt{a}$

Answer 2

$frac{a sqrt{a}+b sqrt{b} }{a- sqrt{ab}+b } = frac{ sqrt{a}^2 sqrt{a}+sqrt{b}^2 sqrt{b} }{a- sqrt{a} sqrt{b} +b } = frac{ sqrt{a}^3+sqrt{b}^3}{a- sqrt{a} sqrt{b} +b } = frac{ (sqrt{a}+sqrt{b})(sqrt{a}^2-sqrt{a}*sqrt{b}+sqrt{b}^2)}{a- sqrt{a} sqrt{b} +b } = \ \ = frac{ (sqrt{a}+sqrt{b})(a-sqrt{a}*sqrt{b}+b)}{a- sqrt{a} sqrt{b} +b } = sqrt{a}+sqrt{b}$