$\begin{array}{l}\phantom{\phantom{;}x^{2}+1;}{\phantom{;}6x^{2}\phantom{-;x^n}-7\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+1\overline{\smash{)}\phantom{;}6x^{4}\phantom{-;x^n}-x^{2}-9x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+1;}\underline{-6x^{4}\phantom{-;x^n}-6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-6x^{4}-6x^{2};}-7x^{2}-9x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+1-;x^n;}\underline{\phantom{;}7x^{2}\phantom{-;x^n}+7\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}7x^{2}+7\phantom{;}\phantom{;}-;x^n;}-9x\phantom{;}+5\phantom{;}\phantom{;}\\\end{array}$

$6x^{2}-7+\frac{-9x+5}{x^2+1}$