Question

Упростите выражение: под буквой в.

Answer 1

$\left ( \frac{a^{\frac{3}{4}}(a+1)^{-\frac{1}{3}}}{a^{\frac{1}{2}}-1} \cdot \frac{a^{\frac{1}{4}}(a-1)^{\frac{1}{3}}}{a^{\frac{1}{2}}+1}\right )^{-\frac{1}{3}}:\frac{(a+1)^{-\frac{8}{9}}}{(a-1)^{\frac{7}{9}}\cdot a^{\frac{4}{3}}}=\\\\=\left (\frac{a(a-1)^{\frac{1}{3}}}{(a+1)^{\frac{1}{3}}(a-1)} \right )^{-\frac{1}{3}}\cdot \frac{(a-1)^{\frac{7}{9}}a^{\frac{4}{3}}}{(a+1)^{-\frac{8}{9}}} =$

$=\left ( \frac{(a+1)^{\frac{1}{3}}(a-1)^{\frac{2}{3}}}{a}\right )^{\frac{1}{3}} \cdot (a-1)^{\frac{7}{9}}a^{\frac{4}{3}}(a+1)^{\frac{8}{9}}=$

$=(a+1)^{\frac{1}{9}}(a-1)^{\frac{2}{9}}\cdot a^{-\frac{1}{3}}(a-1)^{\frac{7}{9}}\cdot a^{\frac{4}{3}}(a+1)^{\frac{8}{9}}=\\\\=(a+1)(a-1)\cdot a=(a^2-1)\cdot a$