Analog divider using OpAmp
The circuit is based on (and can be seen as) a simple inverting opamp circuit.
In general: 

Acl=-Hf/(1/Aol+Hr) and for Aol infinite (ideal opamp) Acl=-Hf/Hr with

Acl: Closed-loop gain, Aol:Open-loop gain 

Hf: Input signal portion available at the inv. input (Vout=0);

Hr: Output signal portion available at the inv. input (Vin=0).

In our case: Hf=1/2 and Hr=Vr/2.

Therefore: H(s)=-1/Vr

Special case: Vr=1 with H(s)=-1 (as known from simple inverter circuit).