$\begin{array}{l}\phantom{\phantom{;}3x^{3}-1;}{\phantom{;}x^{2}\phantom{-;x^n}-\frac{1}{3}\phantom{;}\phantom{;}}\\\phantom{;}3x^{3}-1\overline{\smash{)}\phantom{;}3x^{5}\phantom{-;x^n}-x^{3}\phantom{-;x^n}+x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3x^{3}-1;}\underline{-3x^{5}\phantom{-;x^n}\phantom{-;x^n}+x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{5}+x^{2};}-x^{3}+x^{2}+x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x^{3}-1-;x^n;}\underline{\phantom{;}x^{3}\phantom{-;x^n}\phantom{-;x^n}-\frac{1}{3}\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}x^{3}-\frac{1}{3}\phantom{;}\phantom{;}-;x^n;}\phantom{;}x^{2}+x\phantom{;}-\frac{7}{3}\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-\frac{1}{3}+\frac{x^{2}+x-\frac{7}{3}}{3x^3-1}$