Evaluate the limit: lim_{x to 1} left[ frac{x | vedclass

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(C) Step $1$: Factorize the denominators.$x^2 - x = x(x - 1)$$x^3 - 3x^2 + 2x = x(x^2 - 3x + 2) = x(x - 1)(x - 2)$Step $2$: Combine the fractions.$\fr

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$2$

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(C) Step $1$: Factorize the denominators.$x^2 - x = x(x - 1)$$x^3 - 3x^2 + 2x = x(x^2 - 3x + 2) = x(x - 1)(x - 2)$Step $2$: Combine the fractions.$\frac{x - 2}{x(x - 1)} - \frac{1}{x(x - 1)(x - 2)} = \frac{(x - 2)^2 - 1}{x(x - 1)(x - 2)}$Step $3$: Simplify the numerator.$(x - 2)^2 - 1 = (x^2 - 4x + 4) - 1 = x^2 - 4x + 3 = (x - 1)(x - 3)$Step $4$: Substitute back into the limit expression.$\lim_{x 	o 1} \frac{(x - 1)(x - 3)}{x(x - 1)(x - 2)} = \lim_{x 	o 1} \frac{x - 3}{x(x - 2)}$Step $5$: Evaluate the limit by substituting $x = 1$.$\frac{1 - 3}{1(1 - 2)} = \frac{-2}{-1} = 2$

Evaluate the limit: $\lim_{x \to 1} \left[ \frac{x - 2}{x^2 - x} - \frac{1}{x^3 - 3x^2 + 2x} \right]$

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