MOSFET differential pair with feedback

I’ve been looking deeper into the idea of performing feedback analysis for MOSFET differential pair configurations. This particular amplifier circuit has been giving me some trouble, where I am looking to find the closed-loop gain $(v_{o}/v_{s}) $:

The circuit states that the transconductances of the MOSFETs in the pair are equal but the transconductance of the 3rd MOSFET is not $(g_{M1}=g_{M2}ne g_{M3}) $. Output resistances of the transistors are also taken to be infinity.

If we continue under the assumption that $R_1=R_2$ and perform our standard $Abeta$ feedback analysis, I arrive at the following equations:

$$A=-g_{M3}R_{eq}g_{M1}R_{1},space beta=frac{R_5}{R_5+R_4}$$

where $R_{eq}=(R_{22}||R_3)=((R_4+R_5)||R_3)$ with the final closed-loop gain expression being of the form:

$$left( frac{v_o}{v_s} right)=frac{A}{1+Abeta}$$

Here is my issue. I do not see how the gain can be solved for unless $R_1$ is taken to be equal to $R_2$. This assumption allows us to convert the differential pair into a half circuit and makes solving the $A$ circuit relatively straightforward.

Is this a legitimate assumption though, or can the circuit be solved assuming $R_1ne R_2$?