$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-4;}{\phantom{;}x^{11}+4x^{10}+16x^{9}+64x^{8}+256x^{7}+1024x^{6}+4096x^{5}+16384x^{4}+65536x^{3}+262144x^{2}+1048576x\phantom{;}+4194304\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-4\overline{\smash{)}\phantom{;}x^{12}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-4;}\underline{-x^{12}+4x^{11}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{12}+4x^{11};}\phantom{;}4x^{11}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n;}\underline{-4x^{11}+16x^{10}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-4x^{11}+16x^{10}-;x^n;}\phantom{;}16x^{10}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n;}\underline{-16x^{10}+64x^{9}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-16x^{10}+64x^{9}-;x^n-;x^n;}\phantom{;}64x^{9}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n-;x^n;}\underline{-64x^{9}+256x^{8}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;-64x^{9}+256x^{8}-;x^n-;x^n-;x^n;}\phantom{;}256x^{8}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n-;x^n-;x^n;}\underline{-256x^{8}+1024x^{7}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;;-256x^{8}+1024x^{7}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}1024x^{7}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{-1024x^{7}+4096x^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;;;-1024x^{7}+4096x^{6}-;x^n-;x^n-;x^n-;x^n-;x^n;}\phantom{;}4096x^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{-4096x^{6}+16384x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;;;;-4096x^{6}+16384x^{5}-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\phantom{;}16384x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{-16384x^{5}+65536x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;;;;;-16384x^{5}+65536x^{4}-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\phantom{;}65536x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{-65536x^{4}+262144x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;;;;;;-65536x^{4}+262144x^{3}-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\phantom{;}262144x^{3}\phantom{-;x^n}\phantom{-;x^n}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{-262144x^{3}+1048576x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;;;;;;;-262144x^{3}+1048576x^{2}-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\phantom{;}1048576x^{2}\phantom{-;x^n}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{-1048576x^{2}+4194304x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;;;;;;;;-1048576x^{2}+4194304x\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\phantom{;}4194304x\phantom{;}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{-4194304x\phantom{;}+16777216\phantom{;}\phantom{;}}\\\phantom{;;;;;;;;;;;-4194304x\phantom{;}+16777216\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\phantom{;}16777212\phantom{;}\phantom{;}\\\end{array}$

$x^{11}+4x^{10}+16x^{9}+64x^{8}+256x^{7}+1024x^{6}+4096x^{5}+16384x^{4}+65536x^{3}+262144x^{2}+1048576x+4194304+\frac{16777212}{x-4}$