$\begin{array}{l}\phantom{\phantom{;}a\phantom{;}+1;}{\phantom{;}2a^{4}-2a^{3}+3a^{2}-3a\phantom{;}+8\phantom{;}\phantom{;}}\\\phantom{;}a\phantom{;}+1\overline{\smash{)}\phantom{;}2a^{5}\phantom{-;x^n}+a^{3}\phantom{-;x^n}+5a\phantom{;}-8\phantom{;}\phantom{;}}\\\phantom{\phantom{;}a\phantom{;}+1;}\underline{-2a^{5}-2a^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2a^{5}-2a^{4};}-2a^{4}+a^{3}\phantom{-;x^n}+5a\phantom{;}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}a\phantom{;}+1-;x^n;}\underline{\phantom{;}2a^{4}+2a^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}2a^{4}+2a^{3}-;x^n;}\phantom{;}3a^{3}\phantom{-;x^n}+5a\phantom{;}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}a\phantom{;}+1-;x^n-;x^n;}\underline{-3a^{3}-3a^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-3a^{3}-3a^{2}-;x^n-;x^n;}-3a^{2}+5a\phantom{;}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}a\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{\phantom{;}3a^{2}+3a\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}3a^{2}+3a\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}8a\phantom{;}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}a\phantom{;}+1-;x^n-;x^n-;x^n-;x^n;}\underline{-8a\phantom{;}-8\phantom{;}\phantom{;}}\\\phantom{;;;;-8a\phantom{;}-8\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-16\phantom{;}\phantom{;}\\\end{array}$

$2a^{4}-2a^{3}+3a^{2}-3a+8+\frac{-16}{a+1}$