$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-3;}{\phantom{;}3x^{3}+16x^{2}+43x\phantom{;}+130\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-3\overline{\smash{)}\phantom{;}3x^{4}+7x^{3}-5x^{2}+x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-3;}\underline{-3x^{4}+9x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}+9x^{3};}\phantom{;}16x^{3}-5x^{2}+x\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n;}\underline{-16x^{3}+48x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-16x^{3}+48x^{2}-;x^n;}\phantom{;}43x^{2}+x\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n;}\underline{-43x^{2}+129x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-43x^{2}+129x\phantom{;}-;x^n-;x^n;}\phantom{;}130x\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n-;x^n;}\underline{-130x\phantom{;}+390\phantom{;}\phantom{;}}\\\phantom{;;;-130x\phantom{;}+390\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}384\phantom{;}\phantom{;}\\\end{array}$

$3x^{3}+16x^{2}+43x+130+\frac{384}{x-3}$