To find the limit of the given function as x approaches infinity, we can simplify the expression first by factoring the numerator and the denominator.

Given function: (x^3 - 3x + 2) / (x^2 - 4x + 3)

Factor the numerator:
x^3 - 3x + 2 = (x - 1)(x^2 + x - 2) = (x - 1)(x + 2)(x - 1)

Factor the denominator:
x^2 - 4x + 3 = (x - 1)(x - 3)

Now, the given function becomes: ((x - 1)(x + 2)(x - 1)) / ((x - 1)(x - 3))

Simplify the expression by canceling out (x - 1) from the numerator and the denominator:
= (x + 2) / (x - 3)

As x approaches infinity, the highest order terms in the numerator and the denominator dominate. Therefore, the limit of the function as x approaches infinity is approximately 1.