Question

Para x > 0, a fração $\frac{ 5 \sqrt[3]{ x^{2} } - \sqrt[3]{ x_{5} } } { 5 \sqrt[4]{ x^{3} } - \sqrt[4]{ x^{7} } }$ , simplificada, é igual a:

a) $x^{ \frac{1}{3} }$
b) $x^{ \frac{1}{4} }$
c) $x^{ \frac{1}{6} }$
d) $x^{ \frac{2}{3} }$
e) $x^{ \frac{1}{12} }$

Answer 1

$\frac{5 \sqrt[3]{x^2}-\sqrt[3]{x^5} }{5 \sqrt[4]{x^3}-\sqrt[4]{x^7}}=\\\\\frac{5x^{\frac{2}{3}}-x^{\frac{5}{3}}}{5x^{\frac{3}{4}}-x^{\frac{7}{4}}}=\\\\\frac{x^{\frac{2}{3}}(5-x)}{x^{\frac{3}{4}}(5-x)} =\\\\\frac{x^{\frac{2}{3}}}{x^{\frac{3}{4}}}=\\\\x^{\frac{2}{3}-\frac{3}{4}}=\\\\x^{\frac{8-9}{12}}\\\\x^{\frac{-1}{12}}$