Question

Всем здравствуйте. Нужна помощь с выражением

Answer 1

$(\frac{2}{\sqrt{a}-\sqrt{b}}-\frac{2\sqrt{a}}{a\sqrt{a}+b\sqrt{b}}\cdot \frac{a-\sqrt{ab}+b}{\sqrt{a}-\sqrt{b}}):4\sqrt{b}=\\\\\star \; \; a\sqrt{a}+b\sqrt{b}=\sqrt{a^3}+\sqrt{b^3}=(\sqrt{a})^3+(\sqrt{b})^3=\\=(\sqrt{a}+\sqrt{b})((\sqrt{a})^2-\sqrt{a}\cdot \sqrt{b}+(\sqrt{b})^2)=\\=(\sqrt{a}+\sqrt{b})(a-\sqrt{ab}+b)\; \; \star \\\\=(\frac{2}{\sqrt{a}-\sqrt{b}}-\frac{2\sqrt{a}}{(\sqrt{a}+\sqrt{b})(a-\sqrt{ab}+b)}\cdot \frac{a-\sqrt{ab}+b}{\sqrt{a}-\sqrt{b}})\cdot \frac{1}{4\sqrt{b}}=$

$=(\frac{2}{\sqrt{a}-\sqrt{b}}-\frac{2\sqrt{a}}{(\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b})})\cdot \frac{1}{4\sqrt{b}}= \\\\=\frac{2(\sqrt{a}+\sqrt{b})-2\sqrt{a}}{(\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b})}\cdot \frac{1}{4\sqrt{b}}=\frac{2\sqrt{b}}{(a-b)\cdot 4\sqrt{b}}=\frac{1}{2(a-b)}$