Question

Помогите Упростить выражение

Answer 1

Обозначим 
$\sqrt{a}=x; \ \sqrt{b}=y\Rightarrow \left(\frac{a\sqrt{a}+b\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\right)\cdot \frac{1}{a-b}= \left(\frac{x^3+y^3}{x+y}-xy\right)\cdot \frac{1}{x^2-y^2}=$

$=\left(\frac{(x+y)(x^2-xy+y^2)}{x+y}-xy\right)\cdot \frac{1}{x^2-y^2}= (x^2-xy+y^2-xy)\cdot \frac{1}{x^2-y^2}=$

$=\frac{x^2-2xy+y^2}{x^2-y^2}=\frac{(x-y)^2}{(x-y)(x+y)}=\frac{x-y}{x+y}$

$=\frac{\sqrt{a}-\sqrt{b}}{\sqrt{a}+\sqrt{b}}$