$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-4;}{\phantom{;}3x^{3}+12x^{2}+44x\phantom{;}+179\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-4\overline{\smash{)}\phantom{;}3x^{4}\phantom{-;x^n}-4x^{2}+3x\phantom{;}-7\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-4;}\underline{-3x^{4}+12x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}+12x^{3};}\phantom{;}12x^{3}-4x^{2}+3x\phantom{;}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n;}\underline{-12x^{3}+48x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-12x^{3}+48x^{2}-;x^n;}\phantom{;}44x^{2}+3x\phantom{;}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n;}\underline{-44x^{2}+176x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-44x^{2}+176x\phantom{;}-;x^n-;x^n;}\phantom{;}179x\phantom{;}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n-;x^n;}\underline{-179x\phantom{;}+716\phantom{;}\phantom{;}}\\\phantom{;;;-179x\phantom{;}+716\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}709\phantom{;}\phantom{;}\\\end{array}$

$3x^{3}+12x^{2}+44x+179+\frac{709}{x-4}$