$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-6;}{\phantom{;}4x^{2}+24x\phantom{;}+144\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-6\overline{\smash{)}\phantom{;}4x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}x\phantom{;}-6;}\underline{-4x^{3}+24x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{3}+24x^{2};}\phantom{;}24x^{2}\phantom{-;x^n}\phantom{-;x^n}\\\phantom{\phantom{;}x\phantom{;}-6-;x^n;}\underline{-24x^{2}+144x\phantom{;}\phantom{-;x^n}}\\\phantom{;-24x^{2}+144x\phantom{;}-;x^n;}\phantom{;}144x\phantom{;}\phantom{-;x^n}\\\phantom{\phantom{;}x\phantom{;}-6-;x^n-;x^n;}\underline{-144x\phantom{;}+864\phantom{;}\phantom{;}}\\\phantom{;;-144x\phantom{;}+864\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}864\phantom{;}\phantom{;}\\\end{array}$

$4x^{2}+24x+144+\frac{864}{x-6}$