$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-3;}{\phantom{;}4x^{3}+8x^{2}+26x\phantom{;}+78\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-3\overline{\smash{)}\phantom{;}4x^{4}-4x^{3}+2x^{2}\phantom{-;x^n}-3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-3;}\underline{-4x^{4}+12x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{4}+12x^{3};}\phantom{;}8x^{3}+2x^{2}\phantom{-;x^n}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n;}\underline{-8x^{3}+24x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-8x^{3}+24x^{2}-;x^n;}\phantom{;}26x^{2}\phantom{-;x^n}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n;}\underline{-26x^{2}+78x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-26x^{2}+78x\phantom{;}-;x^n-;x^n;}\phantom{;}78x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n-;x^n;}\underline{-78x\phantom{;}+234\phantom{;}\phantom{;}}\\\phantom{;;;-78x\phantom{;}+234\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}231\phantom{;}\phantom{;}\\\end{array}$

$4x^{3}+8x^{2}+26x+78+\frac{231}{x-3}$