Why is the gain of feedback amplifier Vo/Vs?

Amplification = Output/Input

Then the amplification of the feedback amplifier should be Vo/(Vs +- Vf)

Here,

Vf = feedback signal

Vo = Output signal

Vi = Input Signal and Vi = Vs +- Vf

Vs = Source signal

I have used V instead of phi • Without explaining your symbols you cannot expect a substantial answer. – LvW Nov 20 '18 at 10:12
• Define Vf by drawing a schematic and using words. Not much to ask. – Andy aka Nov 20 '18 at 10:33

Vf is nothing but fraction of output voltage (Vo) that is fed back to the input for various purposes(to increase stability for example) Well let me take op amp example Think of the outer box in picture as black box and u don't know what is inside of it. So for you what u have in hand or what u can measure is Vin and Vout Amplification=Vout/Vin Vf does it's job internally and u don't consider it while writing the gain formula or amplification formula Think of the whole block diagram as an amplifier wherein $$\\Phi_\mathrm{s}\$$ is the input and $$\\Phi_\mathrm{o}\$$ is the output. This is similar to a multi-stage amplifier. The total gain is the output of the second amplifier divided by the input of the first amplifier, which is equal to the product of the gains.