Answer
$(-\infty,-1)\cup(1,2)\cup(3,\infty)$
Work Step by Step
Step 1. Factor the inequality as
$\frac{(x-2)(x+1)}{(x-3)(x-1)}\gt0$,
Step 2. Identify the boundary points as
$x=-1,1,2,3$
Step 3. Using the test points to examine the signs of the left side across the boundary points, we have
$...(+)...(-1)...(-)...(1)...(+)...(2)...(-)...(3)...(+)...$
Thus the solutions are
$(-\infty,-1)\cup(1,2)\cup(3,\infty)$
Step 4. We can express the solutions on a real number line as shown in the figure.
