$\begin{array}{l}\phantom{\phantom{;}x^{2}+6x\phantom{;}+4;}{\phantom{;}x^{2}-6x\phantom{;}+32\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+6x\phantom{;}+4\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+6x\phantom{;}+4;}\underline{-x^{4}-6x^{3}-4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-6x^{3}-4x^{2};}-6x^{3}-4x^{2}\phantom{-;x^n}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+6x\phantom{;}+4-;x^n;}\underline{\phantom{;}6x^{3}+36x^{2}+24x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}6x^{3}+36x^{2}+24x\phantom{;}-;x^n;}\phantom{;}32x^{2}+24x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+6x\phantom{;}+4-;x^n-;x^n;}\underline{-32x^{2}-192x\phantom{;}-128\phantom{;}\phantom{;}}\\\phantom{;;-32x^{2}-192x\phantom{;}-128\phantom{;}\phantom{;}-;x^n-;x^n;}-168x\phantom{;}-126\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-6x+32+\frac{-168x-126}{x^2+6x+4}$