$解:错在对 \sqrt{(x-2)²}的化简,正确计算:$
$∵x=2-\sqrt{3}, ∴x-2<0.\ $
$ \begin{aligned} ∴原式&=\frac{(x-2)^{2} }{x-2} +\frac{\sqrt{(x-2)²}}{x(x-2)}\ \\ &=x-2-\frac{x-2}{x(x-2)}=x-2-\frac{1}{x}\ \\ &=2-\sqrt{3}-2-\frac{1}{2-\sqrt{3}}=-\sqrt {3} -(2+\sqrt {3} )\ \\ &= -\sqrt{3}-2-\sqrt{3}=-2-2\sqrt{3}. \\ \end{aligned}$