## Precalculus (6th Edition) Blitzer

$[-1,1)\cup[2,\infty)$
Step 1. Based on the given inequality $\frac{(x+1)(x-2)}{x-1}\geq0$, we can identify the boundary points as $x=-1,1,2$ Step 2. Using the test points to examine the signs of the left side across the boundary points, we have $...(-)...(-1)...(+)...(1)...(-)...(2)...(+)...$ thus the solutions are $[-1,1)\cup[2,\infty)$ Step 3. We can graph the solution on a real number line as shown in the figure.