Solve for x:
(x+1)/(x-3)>0.
assuming x>3,
x+1 > 0
x > -1
so, any x>3 is a solution
assuming x<3,
x+1 < 0
x < -1
so any x < -1 is also a solution
The entire solution set is thus (-∞,-1)U(3,∞)
Extra credit: why did we have to consider the two separate cases?