$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}6x^{5}+12x^{4}+15x^{3}+30x^{2}+68x\phantom{;}+136\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}6x^{6}\phantom{-;x^n}-9x^{4}\phantom{-;x^n}+8x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-6x^{6}+12x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-6x^{6}+12x^{5};}\phantom{;}12x^{5}-9x^{4}\phantom{-;x^n}+8x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-12x^{5}+24x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-12x^{5}+24x^{4}-;x^n;}\phantom{;}15x^{4}\phantom{-;x^n}+8x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{-15x^{4}+30x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-15x^{4}+30x^{3}-;x^n-;x^n;}\phantom{;}30x^{3}+8x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-30x^{3}+60x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;-30x^{3}+60x^{2}-;x^n-;x^n-;x^n;}\phantom{;}68x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n-;x^n;}\underline{-68x^{2}+136x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;;-68x^{2}+136x\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}136x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{-136x\phantom{;}+272\phantom{;}\phantom{;}}\\\phantom{;;;;;-136x\phantom{;}+272\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n;}\phantom{;}273\phantom{;}\phantom{;}\\\end{array}$

$6x^{5}+12x^{4}+15x^{3}+30x^{2}+68x+136+\frac{273}{x-2}$