$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-3;}{\phantom{;}x^{4}+3x^{3}-14x^{2}-42x\phantom{;}-14\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-3\overline{\smash{)}\phantom{;}x^{5}\phantom{-;x^n}-23x^{3}\phantom{-;x^n}+112x\phantom{;}+96\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-3;}\underline{-x^{5}+3x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}+3x^{4};}\phantom{;}3x^{4}-23x^{3}\phantom{-;x^n}+112x\phantom{;}+96\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n;}\underline{-3x^{4}+9x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-3x^{4}+9x^{3}-;x^n;}-14x^{3}\phantom{-;x^n}+112x\phantom{;}+96\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n;}\underline{\phantom{;}14x^{3}-42x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;\phantom{;}14x^{3}-42x^{2}-;x^n-;x^n;}-42x^{2}+112x\phantom{;}+96\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n-;x^n;}\underline{\phantom{;}42x^{2}-126x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}42x^{2}-126x\phantom{;}-;x^n-;x^n-;x^n;}-14x\phantom{;}+96\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}14x\phantom{;}-42\phantom{;}\phantom{;}}\\\phantom{;;;;\phantom{;}14x\phantom{;}-42\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}54\phantom{;}\phantom{;}\\\end{array}$

$x^{4}+3x^{3}-14x^{2}-42x-14+\frac{54}{x-3}$