$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}x^{3}-3x^{2}+9x\phantom{;}-27\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+81\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-x^{4}-3x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-3x^{3};}-3x^{3}\phantom{-;x^n}\phantom{-;x^n}+81\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}3x^{3}+9x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}3x^{3}+9x^{2}-;x^n;}\phantom{;}9x^{2}\phantom{-;x^n}+81\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{-9x^{2}-27x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-9x^{2}-27x\phantom{;}-;x^n-;x^n;}-27x\phantom{;}+81\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n-;x^n;}\underline{\phantom{;}27x\phantom{;}+81\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}27x\phantom{;}+81\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}162\phantom{;}\phantom{;}\\\end{array}$

$x^{3}-3x^{2}+9x-27+\frac{162}{x+3}$