$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{2}+4x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-x^{2}-x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{2}-x\phantom{;};}\phantom{;}3x\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{-3x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{;-3x\phantom{;}-3\phantom{;}\phantom{;}-;x^n;}-9\phantom{;}\phantom{;}\\\end{array}$

$x+3+\frac{-9}{x+1}$