Question

Упростите выражение

Answer 1

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

$\frac{2a^{\frac{2}{3}}- a^{\frac{1}{6}}(1+a)}{a^{\frac{1}{2}}-1}=$

$\frac{2a^{\frac{4}{6}}- a^{\frac{1}{6}}-a^{\frac{7}{6}}}{a^{\frac{1}{2}}-1}=$

$\frac{a^{\frac{1}{6}}(2a^{\frac{3}{6}}- 1-a)}{a^{\frac{1}{2}}-1}=$

$\frac{-a^{\frac{1}{6}}(a-2a^{\frac{3}{6}}+1)}{a^{\frac{1}{2}}-1}=$

$\frac{-a^{\frac{1}{6}}(a^{\frac{1}{2}}-1)^2}{a^{\frac{1}{2}}-1}=$

$-a^{\frac{1}{6}}(a^{\frac{1}{2}}-1)=$

$\sqrt[6]{a} (1- \sqrt{a})$