Answer
$(-\infty,-3)\cup(4,\infty)$
Work Step by Step
Step 1. Based the inequality $\frac{x-4}{x+3}\gt0$, the boundary points are $x=-3,4$
Step 2. Using test points to examine signs across the boundary points, we have
$...(+)...(-3)...(-)...(4)...(+)...$
Thus the solutions are $x\lt-3$ plus $x\gt4$
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 $(-\infty,-3)\cup(4,\infty)$
