$\begin{array}{l}\phantom{\phantom{;}x^{2}+6x\phantom{;}+6;}{\phantom{;}x^{2}-6x\phantom{;}+30\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+6x\phantom{;}+6\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+6x\phantom{;}+6;}\underline{-x^{4}-6x^{3}-6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-6x^{3}-6x^{2};}-6x^{3}-6x^{2}\phantom{-;x^n}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+6x\phantom{;}+6-;x^n;}\underline{\phantom{;}6x^{3}+36x^{2}+36x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}6x^{3}+36x^{2}+36x\phantom{;}-;x^n;}\phantom{;}30x^{2}+36x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+6x\phantom{;}+6-;x^n-;x^n;}\underline{-30x^{2}-180x\phantom{;}-180\phantom{;}\phantom{;}}\\\phantom{;;-30x^{2}-180x\phantom{;}-180\phantom{;}\phantom{;}-;x^n-;x^n;}-144x\phantom{;}-178\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-6x+30+\frac{-144x-178}{x^2+6x+6}$