Let's assume we have .
The first way to do this is to sketch the graph of and then see where y > 0. By looking at the graph below (hopefully it will load) you can see what the solution set will be: .
The other way:
We wish to find the critical points of the function . These are the points where:
1) The function is 0.
2) The denominator is 0.
3) The function under the radical is 0.
For this function, the only critical points are where the function is 0. So solve:
Divide both sides by 2:
So x = -3 and x = 1 are the critical points.
Now we want to break the real line into intervals and test the inequality on each interval:
So we see the solution set is: as we saw from the graph.