$\begin{array}{l}\phantom{-3a^{2}-6a\phantom{;}+8;}{\phantom{;}a^{3}-2a^{2}+3a\phantom{;}-6\phantom{;}\phantom{;}}\\-3a^{2}-6a\phantom{;}+8\overline{\smash{)}-3a^{5}\phantom{-;x^n}+11a^{3}-16a^{2}\phantom{-;x^n}+32\phantom{;}\phantom{;}}\\\phantom{-3a^{2}-6a\phantom{;}+8;}\underline{\phantom{;}3a^{5}+6a^{4}-8a^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}3a^{5}+6a^{4}-8a^{3};}\phantom{;}6a^{4}+3a^{3}-16a^{2}\phantom{-;x^n}+32\phantom{;}\phantom{;}\\\phantom{-3a^{2}-6a\phantom{;}+8-;x^n;}\underline{-6a^{4}-12a^{3}+16a^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-6a^{4}-12a^{3}+16a^{2}-;x^n;}-9a^{3}\phantom{-;x^n}\phantom{-;x^n}+32\phantom{;}\phantom{;}\\\phantom{-3a^{2}-6a\phantom{;}+8-;x^n-;x^n;}\underline{\phantom{;}9a^{3}+18a^{2}-24a\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}9a^{3}+18a^{2}-24a\phantom{;}-;x^n-;x^n;}\phantom{;}18a^{2}-24a\phantom{;}+32\phantom{;}\phantom{;}\\\phantom{-3a^{2}-6a\phantom{;}+8-;x^n-;x^n-;x^n;}\underline{-18a^{2}-36a\phantom{;}+48\phantom{;}\phantom{;}}\\\phantom{;;;-18a^{2}-36a\phantom{;}+48\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-60a\phantom{;}+80\phantom{;}\phantom{;}\\\end{array}$

$a^{3}-2a^{2}+3a-6+\frac{-60a+80}{-3a^2-6a+8}$