Setting the denominator to zero will break up the domain into 5 parts.
2x2 + x - 6 = 0 ---> (2x - 3)(x + 2) = 0 ---> x = 1.5 and x = -2.
The five parts are: 1) the region below x = -2
2) x = -2 <--- at this point there is a break in the graph
3) the region between x = -2 and x = 1.5
4) x = 1.5 <--- at this point there is a break in the graph
5) the region above x = 1.5
Choose a number in the region below x = -2 --- any number, I chose -5. Place this number into the problem to see
if the answer is above 0 or below 0. It's above 0, so this region "works".
Choose a number in the region between x = -2 and x = 1.5 --- any number, I chose 0. Place this number into the
problem to see if the answer is above 0 or below 0. It's below 0, so this region "doesn't work".
Choose a number in the region above x = 1.5 --- any number, I chose 5. Place this number into the problem to see
if the answer is above 0 or below 0. It's above 0, so this region "works".
So, the answer is: (-infinity, -2) union (1.5, infinity)