how would I find the solution to x/x+2 + 1/x-1 < 3/2
First work with equality:
Solve
x/x+2 + 1/x-1 = 3/2
The roots are -5 and 2.
Draw a sketch and determine the limits of the inequality. See for example:
http://img571.imageshack.us/img571/1562/1291676944.png