Упростить ( (a^2-ab)*(a^-0,5+b^-0,5) ) / ( (a+b+2*sqrt(ab)) * (a^-0,5-b^-0,5) )

Решите задачу:

$\frac{(a^2-ab)*(\frac{1}{\sqrt{a}}+\frac{1}{\sqrt{b}})}{(a+b+2\sqrt{ab})*(\frac{1}{\sqrt{a}}-\frac{1}{\sqrt{b}})}$

$1) (a^2-ab)*(\frac{1}{\sqrt{a}}+\frac{1}{\sqrt{b}})=a(a-b)*(\frac{\sqrt{a}+\sqrt{b}}{\sqrt{a}\sqrt{b}})=\frac{a(a-b)(\sqrt{a}+\sqrt{b})}{\sqrt{a}\sqrt{b}}$

$2) (a+b+2\sqrt{ab})*(\frac{1}{\sqrt{a}}-\frac{1}{\sqrt{b}})=(\sqrt{a}+\sqrt{b})^2*(\frac{\sqrt{b}-\sqrt{a}}{\sqrt{a}\sqrt{b}})= \\ \\ =\frac{(\sqrt{a}+\sqrt{b})^2(\sqrt{b}-\sqrt{a})}{\sqrt{a}\sqrt{b}}=-\frac{(\sqrt{a}+\sqrt{b})^2(\sqrt{a}-\sqrt{b})}{\sqrt{a}\sqrt{b}}$

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