$\begin{array}{l}\phantom{\phantom{;}x^{2}-8;}{\phantom{;}x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-8\overline{\smash{)}\phantom{;}x^{3}+x^{2}-2x\phantom{;}+10\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-8;}\underline{-x^{3}\phantom{-;x^n}+8x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{3}+8x\phantom{;};}\phantom{;}x^{2}+6x\phantom{;}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-8-;x^n;}\underline{-x^{2}\phantom{-;x^n}+8\phantom{;}\phantom{;}}\\\phantom{;-x^{2}+8\phantom{;}\phantom{;}-;x^n;}\phantom{;}6x\phantom{;}+18\phantom{;}\phantom{;}\\\end{array}$

$x+1+\frac{6x+18}{x^2-8}$