$\begin{array}{l}\phantom{\phantom{;}z\phantom{;}+2;}{\phantom{;}z^{5}-2z^{4}+4z^{3}-8z^{2}+16z\phantom{;}-32\phantom{;}\phantom{;}}\\\phantom{;}z\phantom{;}+2\overline{\smash{)}\phantom{;}z^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}z\phantom{;}+2;}\underline{-z^{6}-2z^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-z^{6}-2z^{5};}-2z^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\\\phantom{\phantom{;}z\phantom{;}+2-;x^n;}\underline{\phantom{;}2z^{5}+4z^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}2z^{5}+4z^{4}-;x^n;}\phantom{;}4z^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\\\phantom{\phantom{;}z\phantom{;}+2-;x^n-;x^n;}\underline{-4z^{4}-8z^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-4z^{4}-8z^{3}-;x^n-;x^n;}-8z^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\\\phantom{\phantom{;}z\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}8z^{3}+16z^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}8z^{3}+16z^{2}-;x^n-;x^n-;x^n;}\phantom{;}16z^{2}\phantom{-;x^n}\phantom{-;x^n}\\\phantom{\phantom{;}z\phantom{;}+2-;x^n-;x^n-;x^n-;x^n;}\underline{-16z^{2}-32z\phantom{;}\phantom{-;x^n}}\\\phantom{;;;;-16z^{2}-32z\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-32z\phantom{;}\phantom{-;x^n}\\\phantom{\phantom{;}z\phantom{;}+2-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}32z\phantom{;}+64\phantom{;}\phantom{;}}\\\phantom{;;;;;\phantom{;}32z\phantom{;}+64\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n;}\phantom{;}64\phantom{;}\phantom{;}\\\end{array}$

$z^{5}-2z^{4}+4z^{3}-8z^{2}+16z-32+\frac{64}{z+2}$