$\begin{array}{l}\phantom{\phantom{;}3x^{2}-1;}{\phantom{;}2x^{2}-4x\phantom{;}+\frac{17}{3}\phantom{;}\phantom{;}}\\\phantom{;}3x^{2}-1\overline{\smash{)}\phantom{;}6x^{4}-12x^{3}+15x^{2}+5x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3x^{2}-1;}\underline{-6x^{4}\phantom{-;x^n}+2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-6x^{4}+2x^{2};}-12x^{3}+17x^{2}+5x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x^{2}-1-;x^n;}\underline{\phantom{;}12x^{3}\phantom{-;x^n}-4x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}12x^{3}-4x\phantom{;}-;x^n;}\phantom{;}17x^{2}+x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x^{2}-1-;x^n-;x^n;}\underline{-17x^{2}\phantom{-;x^n}+\frac{17}{3}\phantom{;}\phantom{;}}\\\phantom{;;-17x^{2}+\frac{17}{3}\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}x\phantom{;}+\frac{26}{3}\phantom{;}\phantom{;}\\\end{array}$

$2x^{2}-4x+\frac{17}{3}+\frac{x+\frac{26}{3}}{3x^2-1}$