$\begin{array}{l}\phantom{\phantom{;}2x^{2}-3;}{\phantom{;}2x^{3}-x^{2}+3x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{;}2x^{2}-3\overline{\smash{)}\phantom{;}4x^{5}-2x^{4}\phantom{-;x^n}-x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x^{2}-3;}\underline{-4x^{5}\phantom{-;x^n}+6x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{5}+6x^{3};}-2x^{4}+6x^{3}-x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}-3-;x^n;}\underline{\phantom{;}2x^{4}\phantom{-;x^n}-3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}2x^{4}-3x^{2}-;x^n;}\phantom{;}6x^{3}-4x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}-3-;x^n-;x^n;}\underline{-6x^{3}\phantom{-;x^n}+9x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-6x^{3}+9x\phantom{;}-;x^n-;x^n;}-4x^{2}+9x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}-3-;x^n-;x^n-;x^n;}\underline{\phantom{;}4x^{2}\phantom{-;x^n}-6\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}4x^{2}-6\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}9x\phantom{;}-5\phantom{;}\phantom{;}\\\end{array}$

$2x^{3}-x^{2}+3x-2+\frac{9x-5}{2x^2-3}$