Texas Instruments fully differential op amp app note: I'm having difficulty understanding an equation (single ended to differential video conversion)
The equivalent circuit is this:-



simulate this circuit &ndash; Schematic created using CircuitLab
\$ \frac{R_T}{R_S+R_T}\$ accounts for the voltage division produced by RS (source impedance) and RT (termination resistance). This reduces the input voltage and therefore the gain of the circuit, which is why the term is included in the gain formula.
The values of RG1 and RF are chosen to lower the input impedance to 75 Ω, which further reduces the input voltage (to half the unloaded source voltage). However the op amp gain term \$\frac{R_F}{R_{TH}}\$ already takes this into account because RTH is the combined Thevenin equivalent of RS, RT, and RG1.
Note that unlike an op amp the different amplifier does not create a virtual earth at its inverting input, so its input impedance is not simply RG1. The calculations required to get the desired input impedance and gain are described in TI's app note slyt301 Input impedance matching with fully
differential amplifiers.