Why, in the following immage, the latter two modules, highlighted with purple frame, are partially simplified?
Well, sometimes if you do something like expand before simplify you can confuse the symbolic processor. It's far from perfect. Much more likely though, when you make no assumptions about the domain of the variables the expressions can't be simplified. Unfortunately, I can't open your Prime 3.1 file.and I'm not inclined to retype everything, so that's my best guess.
When I come across problems like this in mathcad, "I go right away on tilt" in the jargon we say .... but I found a loophole to the problem as you can see in the photo: