$\begin{array}{l}\phantom{\phantom{;}2x\phantom{;}+3;}{\phantom{;}x^{3}-2x^{2}+3x\phantom{;}-8\phantom{;}\phantom{;}}\\\phantom{;}2x\phantom{;}+3\overline{\smash{)}\phantom{;}2x^{4}-x^{3}\phantom{-;x^n}-7x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x\phantom{;}+3;}\underline{-2x^{4}-3x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{4}-3x^{3};}-4x^{3}\phantom{-;x^n}-7x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+3-;x^n;}\underline{\phantom{;}4x^{3}+6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}4x^{3}+6x^{2}-;x^n;}\phantom{;}6x^{2}-7x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+3-;x^n-;x^n;}\underline{-6x^{2}-9x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-6x^{2}-9x\phantom{;}-;x^n-;x^n;}-16x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+3-;x^n-;x^n-;x^n;}\underline{\phantom{;}16x\phantom{;}+24\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}16x\phantom{;}+24\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}21\phantom{;}\phantom{;}\\\end{array}$

$x^{3}-2x^{2}+3x-8+\frac{21}{2x+3}$