$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+5;}{\phantom{;}x^{2}-2x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+5\overline{\smash{)}\phantom{;}x^{3}+3x^{2}-4x\phantom{;}-12\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+5;}\underline{-x^{3}-5x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-5x^{2};}-2x^{2}-4x\phantom{;}-12\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n;}\underline{\phantom{;}2x^{2}+10x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}2x^{2}+10x\phantom{;}-;x^n;}\phantom{;}6x\phantom{;}-12\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n-;x^n;}\underline{-6x\phantom{;}-30\phantom{;}\phantom{;}}\\\phantom{;;-6x\phantom{;}-30\phantom{;}\phantom{;}-;x^n-;x^n;}-42\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-2x+6+\frac{-42}{x+5}$