$\begin{array}{l}\phantom{\phantom{;}x^{2}-2;}{\phantom{;}2x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-2\overline{\smash{)}\phantom{;}2x^{3}-3x^{2}+x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-2;}\underline{-2x^{3}\phantom{-;x^n}+4x\phantom{;}\phantom{-;x^n}}\\\phantom{-2x^{3}+4x\phantom{;};}-3x^{2}+5x\phantom{;}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-2-;x^n;}\underline{\phantom{;}3x^{2}\phantom{-;x^n}-6\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}3x^{2}-6\phantom{;}\phantom{;}-;x^n;}\phantom{;}5x\phantom{;}-11\phantom{;}\phantom{;}\\\end{array}$

$2x-3+\frac{5x-11}{x^2-2}$