Question

Помогите упростить второй номер, пожалуйста

Answer 1

$\displaystyle{} \ \ \ \left(\frac{\sqrt[4]{a}(\sqrt[4]{a}-\sqrt[4]{b})^{-1}}{\sqrt[4]{ \frac{b}{a}}+1}- \frac{\sqrt[4]{b}}{(\sqrt[4]{a}+\sqrt[4]{b})\left(\sqrt[4]{\frac{a}{b}}+1\right)-2\sqrt[4]{a}}\right)(a-b)=\\\\\\=\left(\frac{\sqrt[4]{a}}{(\sqrt[4]{a}-\sqrt[4]{b})\left(\frac{\sqrt[4]{b}+\sqrt[4]{a}}{\sqrt[4]{a}}\right)}-\frac{\sqrt[4]{b}}{(\sqrt[4]{a}+\sqrt[4]{b})\left(\frac{\sqrt[4]{a}+\sqrt[4]{b}}{\sqrt[4]{b}}\right)-2\sqrt[4]{a}}\right)(a-b)=$

$\displaystyle =\left(\frac{\sqrt[4]{a}}{\frac{(\sqrt[4]{a}-\sqrt[4]{b})(\sqrt[4]{b}+\sqrt[4]{a})}{\sqrt[4]{a}}}-\frac{\sqrt[4]{b}}{\frac{(\sqrt[4]{a}+\sqrt[4]{b})(\sqrt[4]{a}+\sqrt[4]{b})-2\sqrt[4]{ab}}{\sqrt[4]{b}}}\right)(a-b)=\\\\\\=\left(\frac{\sqrt[4]{a}\cdot\sqrt[4]{a}}{ \sqrt{a}- \sqrt{b}}-\frac{\sqrt[4]{b}\cdot\sqrt[4]{b}}{(\sqrt[4]{a}+\sqrt[4]{b})^2-2\sqrt[4]{ab}} \right)(a-b)=$

$\displaystyle=\left(\frac{\sqrt{a}}{\sqrt{a}- \sqrt{b}}-\frac{\sqrt{b}}{\sqrt{a}+2\sqrt[4]{ab}+\sqrt{b}-2\sqrt[4]{ab}} \right)(a-b)=\\\\\\=\left(\frac{\sqrt{a}}{\sqrt{a}- \sqrt{b}}-\frac{\sqrt{b}}{\sqrt{a}+\sqrt{b}} \right)(a-b)=\\\\\\=\frac{\sqrt{a}(\sqrt{a}+\sqrt{b})-(\sqrt{b}(\sqrt{a}-\sqrt{b}))}{(\sqrt{a}- \sqrt{b})(\sqrt{a}+\sqrt{b})}\cdot (a-b)=\\\\\\=\frac{a+\sqrt{ab}-(\sqrt{ab}-b)}{a-b}\cdot (a-b)=a+\sqrt{ab}-\sqrt{ab}+b=a+b$