When to add two noise amplitudes and when to subtract them?

Hello all,

I found in Razavi's book for eq.(7.96) and (7.97) ""the reader can verify that vny must be subtracted from vnx""

I don't quite get it when to add and when to subtract. In fact, I am quite confused with this chapter on "Noise in Diff Pairs".
Sometimes he adds two noise (amplitude) since they are correlated. Sometimes he doesn't. Indeed, for yet another instance, when discussing Fig 7.46, "does the tail current source in Fig7.44 contribute noise?" I don't quite get it when he wrote "producing only a common-mode noise voltage at the output."

I think the major confusion is how noises are added or subtracted? From the physics point of view, noise is a random thing. So I think they should always be ADDED to account for the worst case when different noise sources don't cancel each other.

I sincerely want your help. Thanks.

Without access to your book, I would guess that the discussion concerns noise cancellation in differential pairs. Regardless of whether noise is random, correlated or whatever, if the same signal is impressed on both lines of a differential pair, the noise will be cancelled by the action of the differential receiver (which SUBTRACTS one input from the other).