So I'd like to solve for \(R_x\) in the standard "reciprocal" formula, where \(R_x\) represents the value of the unknown resistor, and \(R_t\) represents the total resistance of the circuit:

\(R_t=\frac{1}{\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_x}}\)

I have seen the following as a derivation that solves for \(R_x\)...

\(R_x=\frac{1}{\frac{1}{R_t}-\frac{1}{R_2}-\frac{1}{R_3}\)

If this is accurate, then can someone show me the algebraic manipulation to get to it from the original?

Thanks!