Answer
$[-1,1)\cup[2,\infty)$
Work Step by Step
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.
