1/x + 1/x-3 = x-2/x-3

Step 1: Multiply both sides by x.

-3x+2=x2-3x-2

Step 2: Multiply both sides by x.

-3x2+2x=x3-3x2-2x

-3x2+2x - (x3-3x2-2x) = x3-3x2-2x - (x3-3x2-2x) (Subtract x^3-3x^2-2x from both sides)

-x3+4x=0

x (-x+2) (x+2) = 0 (Factor left side of equation)

x=0 or - x+2=0 or x+2=0 (Set factors equal to 0)

x=0 or x=2 or x=-2

Check answers. (Plug them in to make sure they work.)

x=2 (Works in original equation)

x=-2 (Works in original equation)