$\begin{array}{l}\phantom{\phantom{;}x^{2}+1;}{\phantom{;}5x\phantom{;}+7\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+1\overline{\smash{)}\phantom{;}5x^{3}+7x^{2}+x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+1;}\underline{-5x^{3}\phantom{-;x^n}-5x\phantom{;}\phantom{-;x^n}}\\\phantom{-5x^{3}-5x\phantom{;};}\phantom{;}7x^{2}-4x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+1-;x^n;}\underline{-7x^{2}\phantom{-;x^n}-7\phantom{;}\phantom{;}}\\\phantom{;-7x^{2}-7\phantom{;}\phantom{;}-;x^n;}-4x\phantom{;}-8\phantom{;}\phantom{;}\\\end{array}$

$5x+7+\frac{-4x-8}{x^2+1}$