$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-3;}{\phantom{;}x^{2}+3x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-3\overline{\smash{)}\phantom{;}x^{3}\phantom{-;x^n}-6x\phantom{;}-10\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-3;}\underline{-x^{3}+3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}+3x^{2};}\phantom{;}3x^{2}-6x\phantom{;}-10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n;}\underline{-3x^{2}+9x\phantom{;}\phantom{-;x^n}}\\\phantom{;-3x^{2}+9x\phantom{;}-;x^n;}\phantom{;}3x\phantom{;}-10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n;}\underline{-3x\phantom{;}+9\phantom{;}\phantom{;}}\\\phantom{;;-3x\phantom{;}+9\phantom{;}\phantom{;}-;x^n-;x^n;}-1\phantom{;}\phantom{;}\\\end{array}$

$x^{2}+3x+3+\frac{-1}{x-3}$