Question

Объясните, как это решается

Answer 1

$\displaystyle\tt \frac{\sqrt[4]{a}-\sqrt[4]{b}}{\sqrt[8]{a}-\sqrt[8]{b}}-\sqrt[8]{b}=\frac{(\sqrt[8]{a})^2-(\sqrt[8]{b})^2}{\sqrt[8]{a}-\sqrt[8]{b}}-\sqrt[8]{b}=\frac{(\sqrt[8]{a}-\sqrt[8]{b})(\sqrt[8]{a}+\sqrt[8]{b})}{\sqrt[8]{a}-\sqrt[8]{b}}-\sqrt[8]{b}=\\\\\\=\sqrt[8]{a}+\sqrt[8]{b}-\sqrt[8]{b}=\sqrt[8]{a}$

Answer 2

$\star \; \; \sqrt[4]{a}=a^{\frac{1}{4}}=a^{\frac{1}{8}\cdot 2 }=\left (a^{\frac{1}{8}}\right )^2=\Big (\sqrt[8]{a}\Big )^2\; \; \star \\\\\star \; \; A^2-B^2=(A-B)(A+B)\; \; \star \\\\\\\frac{\sqrt[4]{a}-\sqrt[4]{b}}{\sqrt[8]{a}-\sqrt[8]{b}}-\sqrt[8]{b}=\frac{(\sqrt[8]{a}-\sqrt[8]{b})(\sqrt[8]{a}+\sqrt[8]{b})}{\sqrt[8]{a}-\sqrt[8]{b}}-\sqrt[8]{b}=\sqrt[8]{a}+\sqrt[8]{b}-\sqrt[8]{b}=\sqrt[8]{a}$