$\begin{array}{l}\phantom{\phantom{;}x^{2}+1;}{\phantom{;}5x^{2}+6x\phantom{;}-7\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+1\overline{\smash{)}\phantom{;}5x^{4}+6x^{3}-2x^{2}-x\phantom{;}+7\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+1;}\underline{-5x^{4}\phantom{-;x^n}-5x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-5x^{4}-5x^{2};}\phantom{;}6x^{3}-7x^{2}-x\phantom{;}+7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+1-;x^n;}\underline{-6x^{3}\phantom{-;x^n}-6x\phantom{;}\phantom{-;x^n}}\\\phantom{;-6x^{3}-6x\phantom{;}-;x^n;}-7x^{2}-7x\phantom{;}+7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+1-;x^n-;x^n;}\underline{\phantom{;}7x^{2}\phantom{-;x^n}+7\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}7x^{2}+7\phantom{;}\phantom{;}-;x^n-;x^n;}-7x\phantom{;}+14\phantom{;}\phantom{;}\\\end{array}$

$5x^{2}+6x-7+\frac{-7x+14}{x^2+1}$