Question

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

Answer 1

If you mean

x- 1/2 -x -2/3 = 1 , then the x's cancel and you are left with the untrue statement
-7/6 = 1

You need to add parentheses to your equation to clarify the order of algebraic operations.

For example,
(x-1)/2 -(x-2)/3 = 1
is an equation that can be solved. It may or may not be what your question really intended.