$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{-3x^{4}-6x^{3}-17x^{2}-34x\phantom{;}-68\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}-3x^{5}\phantom{-;x^n}-5x^{3}\phantom{-;x^n}\phantom{-;x^n}+4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{\phantom{;}3x^{5}-6x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}3x^{5}-6x^{4};}-6x^{4}-5x^{3}\phantom{-;x^n}\phantom{-;x^n}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{\phantom{;}6x^{4}-12x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}6x^{4}-12x^{3}-;x^n;}-17x^{3}\phantom{-;x^n}\phantom{-;x^n}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{\phantom{;}17x^{3}-34x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;\phantom{;}17x^{3}-34x^{2}-;x^n-;x^n;}-34x^{2}\phantom{-;x^n}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{\phantom{;}34x^{2}-68x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}34x^{2}-68x\phantom{;}-;x^n-;x^n-;x^n;}-68x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}68x\phantom{;}-136\phantom{;}\phantom{;}}\\\phantom{;;;;\phantom{;}68x\phantom{;}-136\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-132\phantom{;}\phantom{;}\\\end{array}$

$-3x^{4}-6x^{3}-17x^{2}-34x-68+\frac{-132}{x-2}$