$\begin{array}{l}\phantom{\phantom{;}x^{2}+6;}{\phantom{;}x^{3}-x^{2}-6x\phantom{;}+7\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+6\overline{\smash{)}\phantom{;}x^{5}-x^{4}\phantom{-;x^n}+x^{2}\phantom{-;x^n}-2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+6;}\underline{-x^{5}\phantom{-;x^n}-6x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}-6x^{3};}-x^{4}-6x^{3}+x^{2}\phantom{-;x^n}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+6-;x^n;}\underline{\phantom{;}x^{4}\phantom{-;x^n}+6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{4}+6x^{2}-;x^n;}-6x^{3}+7x^{2}\phantom{-;x^n}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+6-;x^n-;x^n;}\underline{\phantom{;}6x^{3}\phantom{-;x^n}+36x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}6x^{3}+36x\phantom{;}-;x^n-;x^n;}\phantom{;}7x^{2}+36x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+6-;x^n-;x^n-;x^n;}\underline{-7x^{2}\phantom{-;x^n}-42\phantom{;}\phantom{;}}\\\phantom{;;;-7x^{2}-42\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}36x\phantom{;}-44\phantom{;}\phantom{;}\\\end{array}$

$x^{3}-x^{2}-6x+7+\frac{36x-44}{x^2+6}$