List the critical values of the related function. Then solve the inequality. \[ \frac{x-5}{x+3}-\frac{x+4}{x-2} \leq 0 \] The critical value(s) is/are 0 . (Simplify your answer. Type an integer or a simplified fraction. Type an exact ansu

Step 1 ：Given the inequality \(\frac{x - 5}{x + 3} - \frac{x + 4}{x - 2} \leq 0\)

Step 2 ：Simplify the inequality to get \(\frac{-x^2 + 3x + 2}{(x + 3)(x - 2)} \leq 0\)

Step 3 ：Rewrite the inequality as \(\frac{x^2 - 3x - 2}{(x + 3)(x - 2)} \geq 0\)

Step 4 ：Solve the equation \(x^2 - 3x - 2 = 0\) to get the solutions \(x = 1, 2\)

Step 5 ：Fill in a sign chart for the intervals \(x < -3\), \(-3 < x < 1\), \(1 < x < 2\), and \(2 < x\)

Step 6 ：From the sign chart, we find that the expression is positive when \(x \in (-\infty, -3] \cup [1, 2)\)

Step 7 ：Therefore, the solution to the inequality \(\frac{x^2 - 3x - 2}{(x + 3)(x - 2)} \geq 0\) is \(x \in \boxed{(-\infty, -3] \cup [1, 2)}\)