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

$m^{4}+2m^{3}+4m^{2}+8m+16+\frac{64}{m-2}$