If RD and RE are identical, then the voltage gain from gate to drain is identical to the voltage gain from gate to source, thus providing a pair of outputs identical in amplitude but 180 out of phase.
This circuit has been the subject of much controversy in the audio world because the output impedance (driving point impedance) at the drain is different than at the source. It would seem that if the two outputs (drain and source, or plate and cathode if tubes are used) are loaded with identical impedances, the balance would be upset, but this is not the case.
Yes, my mistake.
This equation Rout=ro * (1 + gm * RE)) I took from the book and it was not a single word about simplification.
So I decided to find Rout by myself.