$\begin{array}{l}\phantom{\phantom{;}3x^{2}-1;}{\phantom{;}x\phantom{;}-\frac{2}{3}\phantom{;}\phantom{;}}\\\phantom{;}3x^{2}-1\overline{\smash{)}\phantom{;}3x^{3}-2x^{2}+3x\phantom{;}-8\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3x^{2}-1;}\underline{-3x^{3}\phantom{-;x^n}+x\phantom{;}\phantom{-;x^n}}\\\phantom{-3x^{3}+x\phantom{;};}-2x^{2}+4x\phantom{;}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x^{2}-1-;x^n;}\underline{\phantom{;}2x^{2}\phantom{-;x^n}-\frac{2}{3}\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}2x^{2}-\frac{2}{3}\phantom{;}\phantom{;}-;x^n;}\phantom{;}4x\phantom{;}-\frac{26}{3}\phantom{;}\phantom{;}\\\end{array}$

$x-\frac{2}{3}+\frac{4x-\frac{26}{3}}{3x^2-1}$