$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-3;}{\phantom{;}4x^{3}+16x^{2}+48x\phantom{;}+143\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-3\overline{\smash{)}\phantom{;}4x^{4}+4x^{3}\phantom{-;x^n}-x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-3;}\underline{-4x^{4}+12x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{4}+12x^{3};}\phantom{;}16x^{3}\phantom{-;x^n}-x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n;}\underline{-16x^{3}+48x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-16x^{3}+48x^{2}-;x^n;}\phantom{;}48x^{2}-x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n;}\underline{-48x^{2}+144x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-48x^{2}+144x\phantom{;}-;x^n-;x^n;}\phantom{;}143x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n-;x^n;}\underline{-143x\phantom{;}+429\phantom{;}\phantom{;}}\\\phantom{;;;-143x\phantom{;}+429\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}430\phantom{;}\phantom{;}\\\end{array}$

$4x^{3}+16x^{2}+48x+143+\frac{430}{x-3}$