(x+1/x-2)×x^2-4/x^3-2x^2+x

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Let's first simplify the expression by factoring out common terms:

((x + 1)/(x - 2)) * x^2 - 4 / (x^3 - 2x^2 + x)

= (x^2 + x) / (x - 2) - 4 / (x^3 - 2x^2 + x)

= x(x + 1) / (x - 2) - 4 / (x(x^2 - 2x + 1))

= x(x + 1) / (x - 2) - 4 / (x(x - 1)^2)

Now, let's find a common denominator and combine the fractions:

= [x(x + 1) x(x - 1)^2 - 4(x - 2)] / [(x - 2) x(x - 1)^2]

= [x^2(x + 1) (x^2 - 2x + 1) - 4(x - 2)] / [(x - 2) x(x - 1)^2]

= [x^3 + x^2 (-2) + x^2 - 2x - 2 + 4x - 8] / [(x - 2) x(x - 1)^2]

= [x^3 - x^2 - 2x - 2] / [(x - 2) * x(x - 1)^2]

Therefore, the simplified expression is (x^3 - x^2 - 2x - 2) / [(x - 2) * x(x - 1)^2].