Answer
$(-\infty,-3]\cup(-1,2]$
Work Step by Step
Step 1. Based on the given inequality $\frac{(x+3)(x-2)}{x+1}\leq0$, the boundary points are $x=-3,-1,2$
Step 2. Using test points to examine signs across the boundary points, we have
$...(-)...(-3)...(+)...(-1)...(-)...(2)...(+)...$
Thus the solutions are $x\leq-3$ or $-1\lt x\leq2$ with the consideration of the equal sign at the boundary points.
Step 3. We can express the solutions on a real number line as shown in the figure.
Step 4. We can express the solutions in interval notation as $(-\infty,-3]\cup(-1,2]$
