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