$\begin{array}{l}\phantom{\phantom{;}4x\phantom{;}+3;}{\phantom{;}x^{2}-2x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;}4x\phantom{;}+3\overline{\smash{)}\phantom{;}4x^{3}-5x^{2}+10x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{\phantom{;}4x\phantom{;}+3;}\underline{-4x^{3}-3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{3}-3x^{2};}-8x^{2}+10x\phantom{;}+6\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x\phantom{;}+3-;x^n;}\underline{\phantom{;}8x^{2}+6x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}8x^{2}+6x\phantom{;}-;x^n;}\phantom{;}16x\phantom{;}+6\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x\phantom{;}+3-;x^n-;x^n;}\underline{-16x\phantom{;}-12\phantom{;}\phantom{;}}\\\phantom{;;-16x\phantom{;}-12\phantom{;}\phantom{;}-;x^n-;x^n;}-6\phantom{;}\phantom{;}\\\end{array}$

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