Answer
$(-4,-3)$
Work Step by Step
Step 1. Based the inequality $\frac{x+3}{x+4}\lt0$, the boundary points are $x=-4,-3$
Step 2. Using test points to examine signs across the boundary points, we have
$...(+)...(-4)...(-)...(-3)...(+)...$
Thus the solutions are $-4\lt x\lt-3$
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 $(-4,-3)$
