Solve 9/x+2 - 1/3x-2 = 2

I assume that we have

  9    -       1

___         _____   =   2              get  a common denominator on the right

x+ 2        3x - 2

9(3x - 2)  - 1(x + 2)

_______________    =  2

  (x + 2) ( 3x - 2)

27x - 18 - 1x - 2

______________     =  2

   (x + 2) (3x - 2)

26x - 20  = 2 (x + 2) (3x - 2)

26x - 20  = 2(3x^2 + 6x - 2x - 4)

26x - 20  =  6x^2 + 8x - 8     rearrange as

6x^2 - 18x + 12  =  0    divide through by 6

x^2 - 3x + 2  = 0   factor

(x - 2) ( x - 1)  = 0

Setting each factor to 0  and solving for x produces  x  = 2  or x = 1