Solve the quadratic inequality \(x^2 - 4x + 3 > 0\).

Step 1 ：Step 1: Rewrite the inequality as \((x-1)(x-3) > 0\) to find the roots of the equation.

Step 2 ：Step 2: Determine the critical points from the roots, which are x = 1 and x = 3.

Step 3 ：Step 3: Make a sign chart and test the intervals (-∞, 1), (1, 3), and (3, ∞) using the inequality \((x-1)(x-3) > 0\).

Step 4 ：Step 4: From the sign chart, we find that \((x-1)(x-3) > 0\) on (-∞, 1) and (3, ∞).