Solve the rational inequality \(\frac{x^2 - 9}{x^2 - 4x + 4} \leq 0\).

Step 1 ：Step 1: First factor the numerator and denominator of the given inequality: \(\frac{(x - 3)(x + 3)}{(x - 2)^2} \leq 0\).

Step 2 ：Step 2: Then, identify the critical points by setting the numerator and denominator equal to zero: \(x - 3 = 0\) gives \(x = 3\), \(x + 3 = 0\) gives \(x = -3\), and \(x - 2 = 0\) gives \(x = 2\).

Step 3 ：Step 3: Plot these critical points on a number line and test a number from each interval to determine where the inequality is satisfied. For instance, at x = -4, 1, 3, and 4, we get positive, negative, positive, and negative values, respectively.

Step 4 ：Step 4: Thus, the solution to the inequality \(\frac{x^2 - 9}{x^2 - 4x + 4} \leq 0\) is \(-3 \leq x < 2\) or \(3 < x\)