$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-6;}{\phantom{;}7x^{3}+30x^{2}+186x\phantom{;}+1112\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-6\overline{\smash{)}\phantom{;}7x^{4}-12x^{3}+6x^{2}-4x\phantom{;}-7\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-6;}\underline{-7x^{4}+42x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-7x^{4}+42x^{3};}\phantom{;}30x^{3}+6x^{2}-4x\phantom{;}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-6-;x^n;}\underline{-30x^{3}+180x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-30x^{3}+180x^{2}-;x^n;}\phantom{;}186x^{2}-4x\phantom{;}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-6-;x^n-;x^n;}\underline{-186x^{2}+1116x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-186x^{2}+1116x\phantom{;}-;x^n-;x^n;}\phantom{;}1112x\phantom{;}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-6-;x^n-;x^n-;x^n;}\underline{-1112x\phantom{;}+6672\phantom{;}\phantom{;}}\\\phantom{;;;-1112x\phantom{;}+6672\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}6665\phantom{;}\phantom{;}\\\end{array}$

$7x^{3}+30x^{2}+186x+1112+\frac{6665}{x-6}$