Rewriting the equation, it is found that the resistance [tex]R_2[/tex] is given by:
[tex]R_2 = \frac{R_TR_1}{R_1 - R_T}[/tex]
The equation given for [tex]R_T[/tex] as function of [tex]R_1[/tex] and [tex]R_2[/tex] is:
[tex]R_T = \frac{R_1R_2}{R_1+R_2}[/tex]
Applying cross multiplication:
[tex]R_TR_1 + R_TR_2 = R_1R_2[/tex]
[tex]R_1R_2 - R_TR_2 = R_TR_1[/tex]
[tex]R_2(R_1 - R_T) = R_TR_1[/tex]
[tex]R_2 = \frac{R_TR_1}{R_1 - R_T}[/tex]
A similar problem is given at https://brainly.com/question/24272167
