Simplify the following expression as much as possible.

$$
\left[x(1-x)^{-\frac{2}{3}}+\frac{x^{2}}{(1-x)^{\frac{5}{3}}}\right]:\left[(1-x)^{\frac{1}{3}}\left(1-2 x+x^{2}\right)^{-1}\right] .
$$
Bring the dividend and divisor to the simplest form.

The dividend, when brought to a common denominator $(x \neq 1)$

$$
\frac{x(1-x)+x^{2}}{(1-x)^{\frac{5}{3}}}=\frac{x}{(1-x)^{\frac{5}{3}}}=x(1-x)^{\frac{5}{3}}
$$

The divisor can be written as:

$$
(1-x)^{-\frac{1}{3}}(1-x)^{-2}=(1-x)^{-\frac{5}{3}}
$$

and thus the quotient

$$
\frac{x(1-x)^{-\frac{5}{3}}}{(1-x)^{-\frac{5}{3}}}=x
$$

Stáhl János (Bp. VI., Kölcsey g. II. o. t.)