The theorem for the addition of velocities given in SR is provably wrong. 

                                V1 + V2 
The theorem gives     V3 = ------------------- 
                              1 + (V1 x V2) 

This violates the conservation of momentum. 

As an example:   The addition of .75c + .75c = .96c 

The momentum (of a one gram mass) for .75c would be 

           1 gr x .75 c 
p = ----------------------- = 1.1339 
       sqrt(1-(v^2/c^2) 

Since both velocities are of a 1 gr mass, the second momentum 
is the same. 

So the combined momenta of the resulting velocity is 2.2678 

The resulting velocity, according to SR, is .96c, and the momentum 
of a one gram mass would be 

         1 gr x .96c 
p = -------------------- = 3.42815 
              .28 

So we see that the addition of the momenta is not commensurate with 
the addition of velocities. 

Therefore the addition is not correct. 

(The correct addition yields .915c)