$\begin{array}{l}\phantom{\phantom{;}x^{2}+x\phantom{;}+6;}{\phantom{;}x^{2}-x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+x\phantom{;}+6\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+x\phantom{;}+6;}\underline{-x^{4}-x^{3}-6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-x^{3}-6x^{2};}-x^{3}-6x^{2}\phantom{-;x^n}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+x\phantom{;}+6-;x^n;}\underline{\phantom{;}x^{3}+x^{2}+6x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{3}+x^{2}+6x\phantom{;}-;x^n;}-5x^{2}+6x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+x\phantom{;}+6-;x^n-;x^n;}\underline{\phantom{;}5x^{2}+5x\phantom{;}+30\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}5x^{2}+5x\phantom{;}+30\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}11x\phantom{;}+32\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-x-5+\frac{11x+32}{x^2+x+6}$