$\begin{array}{l}\phantom{\phantom{;}4x^{2}+5x\phantom{;}+6;}{\phantom{;}x^{2}+2x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;}4x^{2}+5x\phantom{;}+6\overline{\smash{)}\phantom{;}4x^{4}+13x^{3}+28x^{2}+25x\phantom{;}+12\phantom{;}\phantom{;}}\\\phantom{\phantom{;}4x^{2}+5x\phantom{;}+6;}\underline{-4x^{4}-5x^{3}-6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{4}-5x^{3}-6x^{2};}\phantom{;}8x^{3}+22x^{2}+25x\phantom{;}+12\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x^{2}+5x\phantom{;}+6-;x^n;}\underline{-8x^{3}-10x^{2}-12x\phantom{;}\phantom{-;x^n}}\\\phantom{;-8x^{3}-10x^{2}-12x\phantom{;}-;x^n;}\phantom{;}12x^{2}+13x\phantom{;}+12\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x^{2}+5x\phantom{;}+6-;x^n-;x^n;}\underline{-12x^{2}-15x\phantom{;}-18\phantom{;}\phantom{;}}\\\phantom{;;-12x^{2}-15x\phantom{;}-18\phantom{;}\phantom{;}-;x^n-;x^n;}-2x\phantom{;}-6\phantom{;}\phantom{;}\\\end{array}$

$x^{2}+2x+3+\frac{-2x-6}{4x^2+5x+6}$