To solve this inequality, we need to determine the critical points where the expression equals 1.

First, let's simplify the expression by factoring the numerator:

(lg^2x - 3lgx + 3) = (lgx - 1)(lgx - 3)

Therefore, the inequality becomes:

(lgx - 1)(lgx - 3)/(lgx - 1) ≤ 1

Now simplify:

lgx - 3 ≤ 1

lgx ≤ 4

x ≤ 10^4

Therefore, the solution to the inequality is x ≤ 10^4.