Answer
$\frac{3x-5}{(2x-3)^{4/3}}$
Work Step by Step
Start with cancelling the common factor $(2x-3)^{-2/3}$, we have:
$\frac{2(2x-3)^{1/3}-(x-1)(2x-3)^{-2/3}}{(2x-3)^{2/3}}=\frac{2(2x-3)^{1/3+2/3}-(x-1)}{(2x-3)^{2/3+2/3}}=\frac{2(2x-3)-(x-1)}{(2x-3)^{4/3}}=\frac{3x-5}{(2x-3)^{4/3}}$
