Question

(x^(4/3)-x)/(x-x^(5/3))

Answer 1

$\frac{x^{4/3}-x}{x-x^{5/3}}=\frac{x\cdot (x^{1/3}-1)}{x(1-x^{2/3})}=\frac{x^{1/3}-1}{-((x^{1/3})^2-1)}=\frac{x^{1/3}-1}{-(x^{1/3}-1)(x^{1/3}+1)}=\\\\=-\frac{1}{x^{1/3}+1}=-\frac{1}{\sqrt[3]{x}+1}$

Answer 2

(x⁴/³-x)/(x-x⁵/³))=-х(-х¹/³+1)/(х(1-х²/³)=-1/(1+х¹/³)