$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}5x^{3}+7x^{2}-3x\phantom{;}+17\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}5x^{4}-3x^{3}-17x^{2}+23x\phantom{;}+10\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-5x^{4}+10x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-5x^{4}+10x^{3};}\phantom{;}7x^{3}-17x^{2}+23x\phantom{;}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-7x^{3}+14x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-7x^{3}+14x^{2}-;x^n;}-3x^{2}+23x\phantom{;}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{\phantom{;}3x^{2}-6x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}3x^{2}-6x\phantom{;}-;x^n-;x^n;}\phantom{;}17x\phantom{;}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-17x\phantom{;}+34\phantom{;}\phantom{;}}\\\phantom{;;;-17x\phantom{;}+34\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}44\phantom{;}\phantom{;}\\\end{array}$

$5x^{3}+7x^{2}-3x+17+\frac{44}{x-2}$