# Doppler Effect and Relativity

The equation for the Doppler effect is given by

$$f_L = \frac{v+v_L}{v+v_S}f_S$$

where the velocities of both the source and the listener matter. My question is, how does this fit into Galilean relativity? For instance, if a source was moving and the listener is also moving, if I take the reference frame to be that of the listener, change the velocity of the source to a relative velocity I will get a different result. Why is that? Does the equation just not work like that?