$\begin{array}{l}\phantom{\phantom{;}m\phantom{;}+2;}{\phantom{;}m^{6}-2m^{5}+4m^{4}-8m^{3}+16m^{2}-32m\phantom{;}+64\phantom{;}\phantom{;}}\\\phantom{;}m\phantom{;}+2\overline{\smash{)}\phantom{;}m^{7}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-128\phantom{;}\phantom{;}}\\\phantom{\phantom{;}m\phantom{;}+2;}\underline{-m^{7}-2m^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-m^{7}-2m^{6};}-2m^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-128\phantom{;}\phantom{;}\\\phantom{\phantom{;}m\phantom{;}+2-;x^n;}\underline{\phantom{;}2m^{6}+4m^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}2m^{6}+4m^{5}-;x^n;}\phantom{;}4m^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-128\phantom{;}\phantom{;}\\\phantom{\phantom{;}m\phantom{;}+2-;x^n-;x^n;}\underline{-4m^{5}-8m^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-4m^{5}-8m^{4}-;x^n-;x^n;}-8m^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-128\phantom{;}\phantom{;}\\\phantom{\phantom{;}m\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}8m^{4}+16m^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}8m^{4}+16m^{3}-;x^n-;x^n-;x^n;}\phantom{;}16m^{3}\phantom{-;x^n}\phantom{-;x^n}-128\phantom{;}\phantom{;}\\\phantom{\phantom{;}m\phantom{;}+2-;x^n-;x^n-;x^n-;x^n;}\underline{-16m^{3}-32m^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;;-16m^{3}-32m^{2}-;x^n-;x^n-;x^n-;x^n;}-32m^{2}\phantom{-;x^n}-128\phantom{;}\phantom{;}\\\phantom{\phantom{;}m\phantom{;}+2-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}32m^{2}+64m\phantom{;}\phantom{-;x^n}}\\\phantom{;;;;;\phantom{;}32m^{2}+64m\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n;}\phantom{;}64m\phantom{;}-128\phantom{;}\phantom{;}\\\phantom{\phantom{;}m\phantom{;}+2-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{-64m\phantom{;}-128\phantom{;}\phantom{;}}\\\phantom{;;;;;;-64m\phantom{;}-128\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}-256\phantom{;}\phantom{;}\\\end{array}$

$m^{6}-2m^{5}+4m^{4}-8m^{3}+16m^{2}-32m+64+\frac{-256}{m+2}$