Evaluate: limx→2 [(1/x - 2) - (2(2x - 3)/x3 - 3x2 + 2x)]
limx→2 [(1/x - 2) - (2(2x - 3)/x3 - 3x2 + 2x)]
= limx→2 [(1/x - 2) - (2(2x - 3)/x(x - 1)(x - 2))]
= limx→2[(x(x - 1) - 2(2x - 3)/x(x - 1)(x - 2))]
= limx→2 [(x2 - 5x + 6/x(x - 1)(x - 2))]
= limx→2 [((x - 2)(x - 3)/x(x - 1)(x - 2))] [x - 2 ≠ 0]
= limx→2 [(x - 3/x(x - 1))]
= (2 - 3/2(2 - 1)) = -1/2