$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-3;}{\phantom{;}x^{4}-2x^{3}-5x^{2}+14x\phantom{;}+40\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-3\overline{\smash{)}\phantom{;}x^{5}-5x^{4}+x^{3}+29x^{2}-2x\phantom{;}-24\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-3;}\underline{-x^{5}+3x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}+3x^{4};}-2x^{4}+x^{3}+29x^{2}-2x\phantom{;}-24\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n;}\underline{\phantom{;}2x^{4}-6x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}2x^{4}-6x^{3}-;x^n;}-5x^{3}+29x^{2}-2x\phantom{;}-24\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n;}\underline{\phantom{;}5x^{3}-15x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;\phantom{;}5x^{3}-15x^{2}-;x^n-;x^n;}\phantom{;}14x^{2}-2x\phantom{;}-24\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n-;x^n;}\underline{-14x^{2}+42x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;-14x^{2}+42x\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}40x\phantom{;}-24\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n-;x^n-;x^n;}\underline{-40x\phantom{;}+120\phantom{;}\phantom{;}}\\\phantom{;;;;-40x\phantom{;}+120\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}96\phantom{;}\phantom{;}\\\end{array}$

$x^{4}-2x^{3}-5x^{2}+14x+40+\frac{96}{x-3}$