$\begin{array}{l}\phantom{\phantom{;}x^{2}-2;}{\phantom{;}4x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-2\overline{\smash{)}\phantom{;}4x^{3}-2x^{2}+5x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-2;}\underline{-4x^{3}\phantom{-;x^n}+8x\phantom{;}\phantom{-;x^n}}\\\phantom{-4x^{3}+8x\phantom{;};}-2x^{2}+13x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-2-;x^n;}\underline{\phantom{;}2x^{2}\phantom{-;x^n}-4\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}2x^{2}-4\phantom{;}\phantom{;}-;x^n;}\phantom{;}13x\phantom{;}-1\phantom{;}\phantom{;}\\\end{array}$

$4x-2+\frac{13x-1}{x^2-2}$