$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}x^{4}-16x^{3}+48x^{2}-144x\phantom{;}+312\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}x^{5}-13x^{4}\phantom{-;x^n}\phantom{-;x^n}-120x\phantom{;}+83\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-x^{5}-3x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}-3x^{4};}-16x^{4}\phantom{-;x^n}\phantom{-;x^n}-120x\phantom{;}+83\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}16x^{4}+48x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}16x^{4}+48x^{3}-;x^n;}\phantom{;}48x^{3}\phantom{-;x^n}-120x\phantom{;}+83\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{-48x^{3}-144x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-48x^{3}-144x^{2}-;x^n-;x^n;}-144x^{2}-120x\phantom{;}+83\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n-;x^n;}\underline{\phantom{;}144x^{2}+432x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}144x^{2}+432x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}312x\phantom{;}+83\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n-;x^n-;x^n;}\underline{-312x\phantom{;}-936\phantom{;}\phantom{;}}\\\phantom{;;;;-312x\phantom{;}-936\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-853\phantom{;}\phantom{;}\\\end{array}$

$x^{4}-16x^{3}+48x^{2}-144x+312+\frac{-853}{x+3}$