$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}x^{4}+2x^{3}-9x^{2}+9x\phantom{;}-17\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{5}+3x^{4}-7x^{3}\phantom{-;x^n}-8x\phantom{;}+8\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-x^{5}-x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}-x^{4};}\phantom{;}2x^{4}-7x^{3}\phantom{-;x^n}-8x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{-2x^{4}-2x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-2x^{4}-2x^{3}-;x^n;}-9x^{3}\phantom{-;x^n}-8x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{\phantom{;}9x^{3}+9x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;\phantom{;}9x^{3}+9x^{2}-;x^n-;x^n;}\phantom{;}9x^{2}-8x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{-9x^{2}-9x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;-9x^{2}-9x\phantom{;}-;x^n-;x^n-;x^n;}-17x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}17x\phantom{;}+17\phantom{;}\phantom{;}}\\\phantom{;;;;\phantom{;}17x\phantom{;}+17\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}25\phantom{;}\phantom{;}\\\end{array}$

$x^{4}+2x^{3}-9x^{2}+9x-17+\frac{25}{x+1}$