$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}5x\phantom{;}-8\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}5x^{2}+7x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-5x^{2}-15x\phantom{;}\phantom{-;x^n}}\\\phantom{-5x^{2}-15x\phantom{;};}-8x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}8x\phantom{;}+24\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}8x\phantom{;}+24\phantom{;}\phantom{;}-;x^n;}\phantom{;}21\phantom{;}\phantom{;}\\\end{array}$

$5x-8+\frac{21}{x+3}$