Question

Даю 70 Баллов срочно, решит задание на фото

Answer 1

$\frac{\sqrt[3]{a}}{\sqrt[6]{a}}=\sqrt[6]{a}\; \; \; ,\; \; \; \frac{\sqrt[4]{a}-\sqrt{a}}{\sqrt[4]{a}}=\frac{\sqrt[4]{a}\cdot (1-\sqrt[4]{a})}{\sqrt[4]{a}}=1-\sqrt[4]{a}\\\\\\\frac{1-\sqrt[4]{a}}{1-\sqrt{a}}=\frac{1-\sqrt[4]{a}}{(1-\sqrt[4]{a})(1+\sqrt[4]{a})}=\frac{1}{1+\sqrt[4]{a}}\; \; ,\; \; \; \frac{1-\sqrt[3]{a}}{\sqrt[6]{a}+1}=\frac{(1-\sqrt[6]{a})(1+\sqrt[6]{a})}{1+\sqrt[6]{a}}=1-\sqrt[6]{a}\; ,\\\\\\\frac{\sqrt[6]{a}+1}{\sqrt{a}+1}=\frac{\sqrt[6]{a}+1}{(\sqrt[6]{a}+1)(\sqrt[6]{a^2}-\sqrt[6]{a}+1)}=\frac{1}{\sqrt[3]{a}-\sqrt[6]{a}+1}$

$\frac{\sqrt{a}-1}{\sqrt[3]{a}+\sqrt[6]{a}+1}=\frac{(\sqrt[6]{a}-1)(\sqrt[3]{a}+\sqrt[6]{a}+1)}{\sqrt[3]{a}+\sqrt[6]{a}+1}=\sqrt[6]{a}-1\\\\\\\\\frac{\sqrt{a}}{\sqrt[4]{a}}-\frac{\sqrt[4]{a}}{\sqrt{a}}=\sqrt[4]{a}-\frac{1}{\sqrt[4]{a}}=\frac{\sqrt{a}-1}{\sqrt[4]{a}}\\\\\\\frac{\sqrt[6]{a}}{\sqrt[3]{a}}+\frac{1-\sqrt[6]{a}}{\sqrt[6]{a}}=\frac{1}{\sqrt[6]{a}}+\frac{1-\sqrt[6]{a}}{\sqrt[6]{a}}=\frac{2-\sqrt[6]{a}}{\sqrt[6]{a}}=\frac{2}{\sqrt[6]{a}}-1$

$\frac{b}{\sqrt[3]{a}-\sqrt[3]{b}}+\frac{\sqrt[6]{b^5}}{\sqrt[6]{a}-\sqrt[6]{b}}=\frac{b+\sqrt[6]{b^5}(\sqrt[6]{a}+\sqrt[6]{b})}{(\sqrt[6]{a}-\sqrt[6]{b})(\sqrt[6]{a}+\sqrt[6]{b})}=\frac{b+\sqrt[6]{ab^5}+b}{(\sqrt[6]{a}-\sqrt[6]{b})(\sqrt[6]{a}+\sqrt[6]{b})}=\\\\=\frac{2b+\sqrt[6]{ab^5}}{\sqrt[3]{a}-\sqrt[3]{b}}=\frac{\sqrt[6]{b^5}\cdot (2\sqrt[6]{b}+\sqrt[6]{a})}{\sqrt[3]{a}-\sqrt[3]{b}}$