$\begin{array}{l}\phantom{\phantom{;}4x\phantom{;}-3;}{\phantom{;}x^{2}-x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;}4x\phantom{;}-3\overline{\smash{)}\phantom{;}4x^{3}-7x^{2}-21x\phantom{;}+9\phantom{;}\phantom{;}}\\\phantom{\phantom{;}4x\phantom{;}-3;}\underline{-4x^{3}+3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{3}+3x^{2};}-4x^{2}-21x\phantom{;}+9\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x\phantom{;}-3-;x^n;}\underline{\phantom{;}4x^{2}-3x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}4x^{2}-3x\phantom{;}-;x^n;}-24x\phantom{;}+9\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x\phantom{;}-3-;x^n-;x^n;}\underline{\phantom{;}24x\phantom{;}-18\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}24x\phantom{;}-18\phantom{;}\phantom{;}-;x^n-;x^n;}-9\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-x-6+\frac{-9}{4x-3}$