$\begin{array}{l}\phantom{\phantom{;}2x\phantom{;}+3;}{\phantom{;}2x^{2}+2x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{;}2x\phantom{;}+3\overline{\smash{)}\phantom{;}4x^{3}+10x^{2}\phantom{-;x^n}-15\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x\phantom{;}+3;}\underline{-4x^{3}-6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{3}-6x^{2};}\phantom{;}4x^{2}\phantom{-;x^n}-15\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+3-;x^n;}\underline{-4x^{2}-6x\phantom{;}\phantom{-;x^n}}\\\phantom{;-4x^{2}-6x\phantom{;}-;x^n;}-6x\phantom{;}-15\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+3-;x^n-;x^n;}\underline{\phantom{;}6x\phantom{;}+9\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}6x\phantom{;}+9\phantom{;}\phantom{;}-;x^n-;x^n;}-6\phantom{;}\phantom{;}\\\end{array}$

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