$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}x^{2}-3x\phantom{;}+14\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}x^{3}\phantom{-;x^n}+5x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-x^{3}-3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-3x^{2};}-3x^{2}+5x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}3x^{2}+9x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}3x^{2}+9x\phantom{;}-;x^n;}\phantom{;}14x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{-14x\phantom{;}-42\phantom{;}\phantom{;}}\\\phantom{;;-14x\phantom{;}-42\phantom{;}\phantom{;}-;x^n-;x^n;}-43\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-3x+14+\frac{-43}{x+3}$