$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}x^{5}-3x^{4}+9x^{3}-27x^{2}+81x\phantom{;}-243\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}x^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-x^{6}-3x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{6}-3x^{5};}-3x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}3x^{5}+9x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}3x^{5}+9x^{4}-;x^n;}\phantom{;}9x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{-9x^{4}-27x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-9x^{4}-27x^{3}-;x^n-;x^n;}-27x^{3}\phantom{-;x^n}\phantom{-;x^n}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n-;x^n;}\underline{\phantom{;}27x^{3}+81x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}27x^{3}+81x^{2}-;x^n-;x^n-;x^n;}\phantom{;}81x^{2}\phantom{-;x^n}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n-;x^n-;x^n;}\underline{-81x^{2}-243x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;;-81x^{2}-243x\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-243x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}243x\phantom{;}+729\phantom{;}\phantom{;}}\\\phantom{;;;;;\phantom{;}243x\phantom{;}+729\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n;}\phantom{;}726\phantom{;}\phantom{;}\\\end{array}$

$x^{5}-3x^{4}+9x^{3}-27x^{2}+81x-243+\frac{726}{x+3}$