The equation obviously has no solution.

What's the problem you've perceived, exactly?

Cas is computer algebra system. 

Your factor \sqrt(1-beta) is defined over the reals exactly for beta

You might think that x=x+1 has no solution, but multiply by x-1, simplify, and you get x=1 which has the solution x=1. Amazing!

Thank you very much

for your attention and many thanks for your contributions!

http://www.wolframalpha.com/input/?i=plot:+sqrt(1%2B%CE%B2)+sqrt(1-%CE%B2)%2F%CE%B2%3D+sqrt(1-%CE%B2)%2F+sqrt+(1%2B%CE%B2)

It is " an equivalence transformation on your [but] for beta = 1 it is not, because you multiply with 0"

Who teaches the physics teachers that multiplying by zero is as dangerous as dividing by zero ?