Solve the rational inequality \(\frac{x^2 - 3x - 4}{x^2 - x - 2} > 0\).

Step 1 ：Step 1: Factor the numerator and denominator separately. We get \(\frac{(x-4)(x+1)}{(x-2)(x+1)} > 0\).

Step 2 ：Step 2: Cancel out the common factors. Here, we cancel out (x+1) from both numerator and denominator, and we get \(\frac{x-4}{x-2} > 0\).

Step 3 ：Step 3: Find the critical points by setting the numerator and denominator equal to zero separately., we get x = 4 and x = 2.

Step 4 ：Step 4: Test the intervals (-\infty, 2), (2, 4), and (4, \infty) using test points 1, 3, and 5 respectively in the inequality \(\frac{x-4}{x-2} > 0\). The sign of each interval is determined by the sign of the test point when substituted into the inequality.

Step 5 ：Step 5: From the sign chart, we can see that the solution set for the given inequality is (2, 4) \cup (4, \infty).