$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-3;}{\phantom{;}5x^{3}+15x^{2}+46x\phantom{;}+144\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-3\overline{\smash{)}\phantom{;}5x^{4}\phantom{-;x^n}+x^{2}+6x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-3;}\underline{-5x^{4}+15x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-5x^{4}+15x^{3};}\phantom{;}15x^{3}+x^{2}+6x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n;}\underline{-15x^{3}+45x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-15x^{3}+45x^{2}-;x^n;}\phantom{;}46x^{2}+6x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n;}\underline{-46x^{2}+138x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-46x^{2}+138x\phantom{;}-;x^n-;x^n;}\phantom{;}144x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n-;x^n;}\underline{-144x\phantom{;}+432\phantom{;}\phantom{;}}\\\phantom{;;;-144x\phantom{;}+432\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}430\phantom{;}\phantom{;}\\\end{array}$

$5x^{3}+15x^{2}+46x+144+\frac{430}{x-3}$