$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-3;}{\phantom{;}6x^{3}+18x^{2}+56x\phantom{;}+173\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-3\overline{\smash{)}\phantom{;}6x^{4}\phantom{-;x^n}+2x^{2}+5x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-3;}\underline{-6x^{4}+18x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-6x^{4}+18x^{3};}\phantom{;}18x^{3}+2x^{2}+5x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n;}\underline{-18x^{3}+54x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-18x^{3}+54x^{2}-;x^n;}\phantom{;}56x^{2}+5x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n;}\underline{-56x^{2}+168x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-56x^{2}+168x\phantom{;}-;x^n-;x^n;}\phantom{;}173x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n-;x^n;}\underline{-173x\phantom{;}+519\phantom{;}\phantom{;}}\\\phantom{;;;-173x\phantom{;}+519\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}516\phantom{;}\phantom{;}\\\end{array}$

$6x^{3}+18x^{2}+56x+173+\frac{516}{x-3}$