$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}5x\phantom{;}-13\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}5x^{2}-8x\phantom{;}-9\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-5x^{2}-5x\phantom{;}\phantom{-;x^n}}\\\phantom{-5x^{2}-5x\phantom{;};}-13x\phantom{;}-9\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{\phantom{;}13x\phantom{;}+13\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}13x\phantom{;}+13\phantom{;}\phantom{;}-;x^n;}\phantom{;}4\phantom{;}\phantom{;}\\\end{array}$

$5x-13+\frac{4}{x+1}$