2.174. $\frac{x^{3}-6 x^{2}+11 x+6}{\left(x^{3}-4 x^{2}+3 x\right) \cdot|x-2|}$.
Solution.

ODZ: $\left\{\begin{array}{l}x \neq 0, \\ x \neq 1, \\ x \neq 2, \\ x \neq 3 .\end{array}\right.$
$\frac{x^{3}-6 x^{2}+11 x-6}{\left(x^{3}-4 x^{2}+3 x\right) \cdot|x-2|}=\frac{(x-3)(x-2)(x-1)}{x(x-3)(x-1) \cdot|x-2|}=\frac{x-2}{x \cdot|x-2|}=$

$=\left\{\begin{array}{l}-\frac{x-2}{x(x-2)}=-\frac{1}{x} \text { when } x \in(-\infty ; 0) \cup(0 ; 1) \cup(1 ; 2), \\ \frac{x-2}{x(x-2)}=\frac{1}{x} \text { when } x \in(2 ; 3) \cup(3 ; \infty) .\end{array}\right.$

Answer: $-\frac{1}{x}$ when $x \in(-\infty ; 0) \cup(0 ; 1) \cup(1 ; 2) ; \frac{1}{x}$ when $x \in(2 ; 3) \cup(3 ; \infty)$.