This first example command

solve({(x-1)/(2*(x-2)) = 2/(x^2-4)+2*(1/2)}, {x})

will be x=-1.

The second example command

solve({(x-1)/(2*(x-2)) = 2/(x^2-4)+1/2}, {x})

won't give me any answer. I know that there is no solution (in sense x=2 for example) for the second math problem.

How can I tell mapple to show me that x=2 ? (even if it's not inside the definition sum R)

Or, if the simplyfication of the equation would be something like x = x + 2 ...