Answer
$(-\infty,-2)\cup(2,\infty)$.
Work Step by Step
Step 1. For $\frac{(x+5)^2}{(x+2)(x-2)}\ge0\Longrightarrow \frac{(x+5)^2}{(x+2)(x-2)}\ge0$, identify boundary points as $x=-5,-2,2$.
Step 2. Form intervals $(-\infty,-5],[-5,-2),(-2,2),(2,\infty)$.
Step 3. Choose test values for each interval $x=-6,-3,0,3$.
Step 4. Test the inequality to get results: $True,\ True,\ False,\ True$
Step 5. We have the solution $(-\infty,-2)\cup(2,\infty)$.
