$\begin{array}{l}\phantom{\phantom{;}a\phantom{;}-6;}{\phantom{;}a^{2}+6a\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;}a\phantom{;}-6\overline{\smash{)}\phantom{;}a^{3}\phantom{-;x^n}-37a\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}a\phantom{;}-6;}\underline{-a^{3}+6a^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-a^{3}+6a^{2};}\phantom{;}6a^{2}-37a\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}a\phantom{;}-6-;x^n;}\underline{-6a^{2}+36a\phantom{;}\phantom{-;x^n}}\\\phantom{;-6a^{2}+36a\phantom{;}-;x^n;}-a\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}a\phantom{;}-6-;x^n-;x^n;}\underline{\phantom{;}a\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}a\phantom{;}-6\phantom{;}\phantom{;}-;x^n-;x^n;}-7\phantom{;}\phantom{;}\\\end{array}$

$a^{2}+6a-1+\frac{-7}{a-6}$