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

$6x-1+\frac{8x-2}{x^2-1}$