$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-3;}{\phantom{;}3x^{3}+7x^{2}+21x\phantom{;}+62\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-3\overline{\smash{)}\phantom{;}3x^{4}-2x^{3}\phantom{-;x^n}-x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-3;}\underline{-3x^{4}+9x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}+9x^{3};}\phantom{;}7x^{3}\phantom{-;x^n}-x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n;}\underline{-7x^{3}+21x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-7x^{3}+21x^{2}-;x^n;}\phantom{;}21x^{2}-x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n;}\underline{-21x^{2}+63x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-21x^{2}+63x\phantom{;}-;x^n-;x^n;}\phantom{;}62x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n-;x^n;}\underline{-62x\phantom{;}+186\phantom{;}\phantom{;}}\\\phantom{;;;-62x\phantom{;}+186\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}188\phantom{;}\phantom{;}\\\end{array}$

$3x^{3}+7x^{2}+21x+62+\frac{188}{x-3}$