Thanks Todd, but this is not what I want/need.

This is what came out (after correcting your formula, supposing that my correction is correct):

Reduce[{A == (M - N)/M, B == M + N, Z*(M - N)/(1 + Z*M + Z*B) == A*(1/(1/(Z*M) + F3))}, F3]

(M == N && 1 + 3 N Z + F3 N Z + 3 F3 N^2 Z^2 != 0) || (N == 0 &&

M == 0) || (M != 0 && F3 == (2 M + N)/M && 1 + 2 M Z + N Z != 0) ||

Z == 0

And this still looks ugly as hell.

The goal I want to get to above, is, the formula has a prefactor A (important), and the rest (which is kind of a correction factor) got rid of the B .

I would expect a command like Replace[H1, (M-N)/M -> A] which should result in H2.

But this gives only:

Replace[H1, (M - N)/M -> A]

((M - N) Z)/(1 + M Z + (M + N) Z)

Remark: All variables are >0 and M>N (but this is a minor detail).