Answer
$(-\infty,-2)\cup(6,\infty)$
Work Step by Step
Step 1. Based on the given inequality $\frac{x-6}{x+2}\gt0$, we can identify the boundary points as $x=-2,6$
Step 2. Using test points to examine the signs of the left side across the boundary points, we have $...(+)...(-2)...(-)...(6)...(+)...$; thus the solutions are $(-\infty,-2)\cup(6,\infty)$
Step 3. We can graph the solution on a real number line as shown in the figure.
