x/x-2 + x-1/x+1 =-1

Question

How do I solve this?

Answer 1

Use a common denominator, just as you do when you figure 1/3 + 1/4
Here, that will be (x-2)(x+1). So, multiply through by that and you get

x(x+1) + (x-1)(x-2) = -1(x+1)(x-2)
expand and collect terms and you wind up with
3x^2 - 3x = 0
3x(x-1) = 0
x = 0,1