Did I solve this complex rational expression correctly?

Question

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

Answer 1

I find it simpler just to clear the fractions

(2/3 - x)/(2/3 + x)
multiply top and bottom by 3 and you have
(2-3x)/(2+3x)

Your final answer is clearly wrong, since you have 3x-2 top and bottom, making the value just -1.