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

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вопрос

To simplify the expression, we first need to factor the denominators of the fractions where possible:

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

Now, we can rewrite the expression and simplify:

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

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

= 3/(x-2) - 3(x+2)(x-1)/((x-1)^2(x+2)(x-2))

= 3/(x-2) - 3x(x+2)/((x-1)(x+2)(x-2))

= 3/(x-2) - 3x/(x-1)

Therefore, the simplified expression is 3/(x-2) - 3x/(x-1).