Simplify fractional indices

Using real cube roots, negative powers require $y\ne0$. The denominator vanishes at $y=\pm1$, so also exclude these values.

$y^{2/3}-y^{-2/3}=y^{2/3}(1-y^{-4/3})=-y^{2/3}(y^{-4/3}-1)$. Hence the quotient is $-y^{2/3}$ on its original domain.