$${ x }^{ 3 } -2x+ \frac{ 1 }{ x-1 }$$
$\frac{x^{4}-x^{3}-2x^{2}+2x+1}{x-1}$
$$\frac{\left(x^{3}-2x\right)\left(x-1\right)}{x-1}+\frac{1}{x-1}$$
$$\frac{\left(x^{3}-2x\right)\left(x-1\right)+1}{x-1}$$
$$\frac{x^{4}-x^{3}-2x^{2}+2x+1}{x-1}$$
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$\frac{3x^{4}-6x^{3}+x^{2}+4x-3}{\left(x-1\right)^{2}}$
