$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-6;}{\phantom{;}x^{3}+4x^{2}+24x\phantom{;}+144\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-6\overline{\smash{)}\phantom{;}x^{4}-2x^{3}\phantom{-;x^n}\phantom{-;x^n}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-6;}\underline{-x^{4}+6x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+6x^{3};}\phantom{;}4x^{3}\phantom{-;x^n}\phantom{-;x^n}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-6-;x^n;}\underline{-4x^{3}+24x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-4x^{3}+24x^{2}-;x^n;}\phantom{;}24x^{2}\phantom{-;x^n}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-6-;x^n-;x^n;}\underline{-24x^{2}+144x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-24x^{2}+144x\phantom{;}-;x^n-;x^n;}\phantom{;}144x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-6-;x^n-;x^n-;x^n;}\underline{-144x\phantom{;}+864\phantom{;}\phantom{;}}\\\phantom{;;;-144x\phantom{;}+864\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}867\phantom{;}\phantom{;}\\\end{array}$

$x^{3}+4x^{2}+24x+144+\frac{867}{x-6}$