$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+6;}{-12x^{3}+79x^{2}-474x\phantom{;}+2844\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+6\overline{\smash{)}-12x^{4}+7x^{3}\phantom{-;x^n}\phantom{-;x^n}-5\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+6;}\underline{\phantom{;}12x^{4}+72x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}12x^{4}+72x^{3};}\phantom{;}79x^{3}\phantom{-;x^n}\phantom{-;x^n}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+6-;x^n;}\underline{-79x^{3}-474x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-79x^{3}-474x^{2}-;x^n;}-474x^{2}\phantom{-;x^n}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+6-;x^n-;x^n;}\underline{\phantom{;}474x^{2}+2844x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}474x^{2}+2844x\phantom{;}-;x^n-;x^n;}\phantom{;}2844x\phantom{;}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+6-;x^n-;x^n-;x^n;}\underline{-2844x\phantom{;}-17064\phantom{;}\phantom{;}}\\\phantom{;;;-2844x\phantom{;}-17064\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-17069\phantom{;}\phantom{;}\\\end{array}$

$-12x^{3}+79x^{2}-474x+2844+\frac{-17069}{x+6}$