$\begin{array}{l}\phantom{\phantom{;}a\phantom{;}+1;}{-a^{6}+a^{5}-a^{4}+a^{3}-a^{2}+a\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;}a\phantom{;}+1\overline{\smash{)}-a^{7}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}a\phantom{;}+1;}\underline{\phantom{;}a^{7}+a^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}a^{7}+a^{6};}\phantom{;}a^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}a\phantom{;}+1-;x^n;}\underline{-a^{6}-a^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-a^{6}-a^{5}-;x^n;}-a^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}a\phantom{;}+1-;x^n-;x^n;}\underline{\phantom{;}a^{5}+a^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;\phantom{;}a^{5}+a^{4}-;x^n-;x^n;}\phantom{;}a^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}a\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{-a^{4}-a^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;-a^{4}-a^{3}-;x^n-;x^n-;x^n;}-a^{3}\phantom{-;x^n}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}a\phantom{;}+1-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}a^{3}+a^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;;\phantom{;}a^{3}+a^{2}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}a^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}a\phantom{;}+1-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{-a^{2}-a\phantom{;}\phantom{-;x^n}}\\\phantom{;;;;;-a^{2}-a\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n;}-a\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}a\phantom{;}+1-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}a\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{;;;;;;\phantom{;}a\phantom{;}+1\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\phantom{;}2\phantom{;}\phantom{;}\\\end{array}$

$-a^{6}+a^{5}-a^{4}+a^{3}-a^{2}+a-1+\frac{2}{1+a}$