$\begin{array}{l}\phantom{\phantom{;}x^{2}+2;}{\phantom{;}2x^{2}-x\phantom{;}-4\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+2\overline{\smash{)}\phantom{;}2x^{4}-x^{3}\phantom{-;x^n}+7x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+2;}\underline{-2x^{4}\phantom{-;x^n}-4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{4}-4x^{2};}-x^{3}-4x^{2}+7x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+2-;x^n;}\underline{\phantom{;}x^{3}\phantom{-;x^n}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{3}+2x\phantom{;}-;x^n;}-4x^{2}+9x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+2-;x^n-;x^n;}\underline{\phantom{;}4x^{2}\phantom{-;x^n}+8\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}4x^{2}+8\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}9x\phantom{;}+5\phantom{;}\phantom{;}\\\end{array}$

$2x^{2}-x-4+\frac{9x+5}{x^2+2}$