If the equation x / x-3-2m + 1 = m / x-3 has only one real solution, then the value range of M

If the equation x / x-3-2m + 1 = m / x-3 has only one real solution, then the value range of M

The original formula of X / (x-3) - 2m + 1 = m / (x-3) should be like this
So first, m ≠ 3, then x + (x-3) (- 2m + 1) = M
(-2m+2)x+5m-3=0
The result is: m ≠ 1
If M ≠ 3 and m ≠ 1
That should be it, right?