$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}3x^{3}+25x^{2}+72x\phantom{;}+138\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}3x^{4}+19x^{3}+22x^{2}-6x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-3x^{4}+6x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}+6x^{3};}\phantom{;}25x^{3}+22x^{2}-6x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-25x^{3}+50x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-25x^{3}+50x^{2}-;x^n;}\phantom{;}72x^{2}-6x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{-72x^{2}+144x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-72x^{2}+144x\phantom{;}-;x^n-;x^n;}\phantom{;}138x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-138x\phantom{;}+276\phantom{;}\phantom{;}}\\\phantom{;;;-138x\phantom{;}+276\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}280\phantom{;}\phantom{;}\\\end{array}$

$3x^{3}+25x^{2}+72x+138+\frac{280}{x-2}$