$\begin{array}{l}\phantom{\phantom{;}3x^{2}-1;}{\frac{2}{3}x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;}3x^{2}-1\overline{\smash{)}\phantom{;}2x^{3}-3x^{2}+5x\phantom{;}-4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3x^{2}-1;}\underline{-2x^{3}\phantom{-;x^n}+\frac{2}{3}x\phantom{;}\phantom{-;x^n}}\\\phantom{-2x^{3}+\frac{2}{3}x\phantom{;};}-3x^{2}+\frac{17}{3}x\phantom{;}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x^{2}-1-;x^n;}\underline{\phantom{;}3x^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}3x^{2}-1\phantom{;}\phantom{;}-;x^n;}\frac{17}{3}x\phantom{;}-5\phantom{;}\phantom{;}\\\end{array}$

$\frac{2}{3}x-1+\frac{\frac{17}{3}x-5}{3x^2-\frac{1}{4}x-1}$