$\begin{array}{l}\phantom{\phantom{;}4x^{2}+x\phantom{;}-6;}{\phantom{;}4x^{3}-x^{2}+6x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{;}4x^{2}+x\phantom{;}-6\overline{\smash{)}\phantom{;}16x^{5}\phantom{-;x^n}-x^{3}\phantom{-;x^n}-40x\phantom{;}+16\phantom{;}\phantom{;}}\\\phantom{\phantom{;}4x^{2}+x\phantom{;}-6;}\underline{-16x^{5}-4x^{4}+24x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-16x^{5}-4x^{4}+24x^{3};}-4x^{4}+23x^{3}\phantom{-;x^n}-40x\phantom{;}+16\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x^{2}+x\phantom{;}-6-;x^n;}\underline{\phantom{;}4x^{4}+x^{3}-6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}4x^{4}+x^{3}-6x^{2}-;x^n;}\phantom{;}24x^{3}-6x^{2}-40x\phantom{;}+16\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x^{2}+x\phantom{;}-6-;x^n-;x^n;}\underline{-24x^{3}-6x^{2}+36x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-24x^{3}-6x^{2}+36x\phantom{;}-;x^n-;x^n;}-12x^{2}-4x\phantom{;}+16\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x^{2}+x\phantom{;}-6-;x^n-;x^n-;x^n;}\underline{\phantom{;}12x^{2}+3x\phantom{;}-18\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}12x^{2}+3x\phantom{;}-18\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-x\phantom{;}-2\phantom{;}\phantom{;}\\\end{array}$

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