$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}3x^{3}-4x^{2}+6x\phantom{;}-13\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}3x^{4}-x^{3}+2x^{2}-7x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-3x^{4}-3x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}-3x^{3};}-4x^{3}+2x^{2}-7x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{\phantom{;}4x^{3}+4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}4x^{3}+4x^{2}-;x^n;}\phantom{;}6x^{2}-7x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{-6x^{2}-6x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-6x^{2}-6x\phantom{;}-;x^n-;x^n;}-13x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{\phantom{;}13x\phantom{;}+13\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}13x\phantom{;}+13\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}12\phantom{;}\phantom{;}\\\end{array}$

$3x^{3}-4x^{2}+6x-13+\frac{12}{x+1}$