$\begin{array}{l}\phantom{\phantom{;}x^{2}-2;}{\phantom{;}3x^{3}\phantom{-;x^n}+6x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-2\overline{\smash{)}\phantom{;}3x^{5}\phantom{-;x^n}\phantom{-;x^n}+4x^{2}-12x\phantom{;}-17\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-2;}\underline{-3x^{5}\phantom{-;x^n}+6x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{5}+6x^{3};}\phantom{;}6x^{3}+4x^{2}-12x\phantom{;}-17\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-2-;x^n;}\underline{-6x^{3}\phantom{-;x^n}+12x\phantom{;}\phantom{-;x^n}}\\\phantom{;-6x^{3}+12x\phantom{;}-;x^n;}\phantom{;}4x^{2}\phantom{-;x^n}-17\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-2-;x^n-;x^n;}\underline{-4x^{2}\phantom{-;x^n}+8\phantom{;}\phantom{;}}\\\phantom{;;-4x^{2}+8\phantom{;}\phantom{;}-;x^n-;x^n;}-9\phantom{;}\phantom{;}\\\end{array}$

$3x^{3}+6x+4+\frac{-9}{x^2-2}$