$\begin{array}{l}\phantom{\phantom{;}x^{2}-1;}{\phantom{;}3x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-1\overline{\smash{)}\phantom{;}3x^{3}-6x^{2}+3x\phantom{;}-4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-1;}\underline{-3x^{3}\phantom{-;x^n}+3x\phantom{;}\phantom{-;x^n}}\\\phantom{-3x^{3}+3x\phantom{;};}-6x^{2}+6x\phantom{;}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-1-;x^n;}\underline{\phantom{;}6x^{2}\phantom{-;x^n}-6\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}6x^{2}-6\phantom{;}\phantom{;}-;x^n;}\phantom{;}6x\phantom{;}-10\phantom{;}\phantom{;}\\\end{array}$

$3x-6+\frac{6x-10}{x^2-1}$