$\begin{array}{l}\phantom{\phantom{;}x^{2}+2;}{\phantom{;}4x^{2}\phantom{-;x^n}-13\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+2\overline{\smash{)}\phantom{;}4x^{4}\phantom{-;x^n}-5x^{2}+8x\phantom{;}-10\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+2;}\underline{-4x^{4}\phantom{-;x^n}-8x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{4}-8x^{2};}-13x^{2}+8x\phantom{;}-10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+2-;x^n;}\underline{\phantom{;}13x^{2}\phantom{-;x^n}+26\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}13x^{2}+26\phantom{;}\phantom{;}-;x^n;}\phantom{;}8x\phantom{;}+16\phantom{;}\phantom{;}\\\end{array}$

$4x^{2}-13+\frac{8x+16}{x^2+2}$