$\begin{array}{l}\phantom{\phantom{;}x^{2}+2;}{\phantom{;}x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+2\overline{\smash{)}\phantom{;}x^{3}+2x^{2}-5x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+2;}\underline{-x^{3}\phantom{-;x^n}-2x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{3}-2x\phantom{;};}\phantom{;}2x^{2}-7x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+2-;x^n;}\underline{-2x^{2}\phantom{-;x^n}-4\phantom{;}\phantom{;}}\\\phantom{;-2x^{2}-4\phantom{;}\phantom{;}-;x^n;}-7x\phantom{;}-3\phantom{;}\phantom{;}\\\end{array}$

$x+2+\frac{-7x-3}{x^2+2}$