A = \(\left(\dfrac{1}{x-1}-\dfrac{1}{x}\right):\left(\dfrac{x+1}{x-2}-\dfrac{x+2}{x-1}\right)\)
= \(\dfrac{x-x+1}{x\left(x-1\right)}:\dfrac{\left(x-1\right)\left(x+1\right)-\left(x-2\right)\left(x+2\right)}{\left(x-1\right)\left(x-2\right)}\)
= \(\dfrac{1}{x\left(x-1\right)}:\dfrac{x^2-1-x^2+4}{\left(x-1\right)\left(x-2\right)}\)
= \(\dfrac{1}{x\left(x-1\right)}.\dfrac{\left(x-1\right)\left(x-2\right)}{3}=\dfrac{\left(x-2\right)}{3x}\)
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