Simplify the rational expression \( \frac{2x^2 - 5x - 3}{x^2 - 4} \)

Step 1 ：First, we factor the numerator and denominator. The numerator factors to \(2x^2 - 5x - 3 = (2x + 1)(x - 3)\) and the denominator factors to \(x^2 - 4 = (x - 2)(x + 2)\)

Step 2 ：So, our expression becomes \( \frac{(2x + 1)(x - 3)}{(x - 2)(x + 2)} \)

Step 3 ：We cannot simplify this any further because none of the factors in the numerator are the same as the factors in the denominator. Therefore, the expression is already in simplest form.