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

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