$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}x^{4}-3x^{3}+9x^{2}-27x\phantom{;}+84\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+3x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-x^{5}-3x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}-3x^{4};}-3x^{4}\phantom{-;x^n}\phantom{-;x^n}+3x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}3x^{4}+9x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}3x^{4}+9x^{3}-;x^n;}\phantom{;}9x^{3}\phantom{-;x^n}+3x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{-9x^{3}-27x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-9x^{3}-27x^{2}-;x^n-;x^n;}-27x^{2}+3x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n-;x^n;}\underline{\phantom{;}27x^{2}+81x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}27x^{2}+81x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}84x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n-;x^n-;x^n;}\underline{-84x\phantom{;}-252\phantom{;}\phantom{;}}\\\phantom{;;;;-84x\phantom{;}-252\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-253\phantom{;}\phantom{;}\\\end{array}$

$x^{4}-3x^{3}+9x^{2}-27x+84+\frac{-253}{x+3}$