Question

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

Answer 1

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

Answer 2

$\sqrt{b} + \sqrt{a}$