$\begin{array}{l}\phantom{\phantom{;}3x^{3}+4x\phantom{;}-1;}{\phantom{;}2x^{2}\phantom{-;x^n}-\frac{8}{3}\phantom{;}\phantom{;}}\\\phantom{;}3x^{3}+4x\phantom{;}-1\overline{\smash{)}\phantom{;}6x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-4x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3x^{3}+4x\phantom{;}-1;}\underline{-6x^{5}\phantom{-;x^n}-8x^{3}+2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-6x^{5}-8x^{3}+2x^{2};}-8x^{3}+2x^{2}-4x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x^{3}+4x\phantom{;}-1-;x^n;}\underline{\phantom{;}8x^{3}\phantom{-;x^n}+\frac{32}{3}x\phantom{;}-\frac{8}{3}\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}8x^{3}+\frac{32}{3}x\phantom{;}-\frac{8}{3}\phantom{;}\phantom{;}-;x^n;}\phantom{;}2x^{2}+\frac{20}{3}x\phantom{;}-\frac{2}{3}\phantom{;}\phantom{;}\\\end{array}$

$2x^{2}-\frac{8}{3}+\frac{2x^{2}+\frac{20}{3}x-\frac{2}{3}}{3x^3+4x-1}$