It would be best if you were to enclose each denominator inside parentheses. Otherwise I have to take an educated guess regarding what you meant:
1 1 x - 2
1/x+1/x-3=x-2/x-3 => ----- + ------ = ----------
x x-3 x - 3
The LCD here is x(x-3).
x-3 x x(x-2)
------- + --------- = -------------
LCD LCD LCD
Then x-3+x=x^2 -3x, or 2x-3=x^2-3x or x^2 - 5x - 3 = 0
Using the quadratic formula to solve for x:
5 plus or minus sqrt(25-4(1)(-3)
x = --------------------------------------------
2
5 plus or minus sqrt( 25 + 12)
= --------------------------------------------
2
There are 2 solutions. Complete the arithmetic to find them.
Be sure to check both answers via subst. into the original equation.