steps would be:
1. get to the common denominator (yes, you have to find this first)
2. simplify
3. put all the number to one side, so you have 0 on the other side of the equation
4. simplify if you need to
5. you are going to have a quadratic function divided by (3-x)(x+1)
6. Solve the quadratic equation (just drop the denominator for now).
7. you would probably use a quadratic formula for that (if you don't remember what it is Google does, this is why I use the name).
8. If this is all you need, you have (x - something)(x - something else)/(3-x)(x+1) = 0
and your answers would be this "something" and "something else"
However if you need to plot your answer, the points x=3 and x = -1 are very important, so try not to lose them during the solution.
Please let me know if you need more explanation.