Answer
$(-3,2)$
Work Step by Step
Step 1. Rewrite the inequality as
$\frac{3}{x+3}-\frac{3}{x-2}\gt0$, $\frac{3x-6-3x-9}{(x+3)(x-2)}\gt0$
and
$\frac{-15}{(x+3)(x-2)}\gt0$,
Step 2. Reorder the inequality; we have
$\frac{15}{(x+3)(x-2)}\lt0$
and the boundary points are
$x=-3, 2$
Step 3. Using test points to examine signs of the left side across the boundary points, we have
$...(+)...(-3)...(-)...(2)...(+)...$
thus the solutions are
$-3\lt x\lt 2$; that is, $(-3,2)$
Step 4. We can express the solutions on a real number line as shown in the figure.
