Out=(-a+x) Im[1/ Sqrt[Abs[b-x]]]
a,b,x are real. The difference x-b is also real.
Abs[x-b] it is real and positive.
Therefore: (1 / Sqrt[Abs[b-x]]) it is real and positive.
Therefore the image is zero
Because it doesn't return:
Im[(x-a)/Sqrt[Abs[x-b]]] = 0 ?
How to attribute the 'x' the condition of real number?
Simplify[#,x=Real] & it doesn't work.