I was just reviewing the Doppler effect, and I thought of something :

the formula involves (v-vr)/(v-vs)

let's say v = 300

vr = 30

vs = 0 (stationary observer)

it will be equal to 270/300

however, if we take the opposite, i.e. consider the reference frame to be that the source is moving not the observer we get

330/300

The 2 are obviously not equal, so is the formula just an approximation?