$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}x^{2}-3x\phantom{;}+13\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}x^{3}\phantom{-;x^n}+4x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-x^{3}-3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-3x^{2};}-3x^{2}+4x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}3x^{2}+9x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}3x^{2}+9x\phantom{;}-;x^n;}\phantom{;}13x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{-13x\phantom{;}-39\phantom{;}\phantom{;}}\\\phantom{;;-13x\phantom{;}-39\phantom{;}\phantom{;}-;x^n-;x^n;}-36\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-3x+13+\frac{-36}{x+3}$