Question

Всем здравствуйте. Нужна помощь с выражением

Answer 1

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

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