$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}3x^{2}+10x\phantom{;}-23\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}3x^{3}+13x^{2}-13x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-3x^{3}-3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{3}-3x^{2};}\phantom{;}10x^{2}-13x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{-10x^{2}-10x\phantom{;}\phantom{-;x^n}}\\\phantom{;-10x^{2}-10x\phantom{;}-;x^n;}-23x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{\phantom{;}23x\phantom{;}+23\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}23x\phantom{;}+23\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}25\phantom{;}\phantom{;}\\\end{array}$

$3x^{2}+10x-23+\frac{25}{x+1}$