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[itex]

T_2 \cdot \frac{R_1}{R_1+R_2} + T_1 \cdot \frac{R_2}{R_1+R_2} [/itex]

and

[itex]T_2 \cdot k_1 + T_1 \cdot k_2[/itex]

I compare and set

[itex]k_1 = \frac{R_1}{R_1+R_2} (1)[/itex]

[itex]k_2 = \frac{R_2}{R_1+R_2} (2)[/itex]

I expand the equations and throw them around

[itex](1) -> R_1 = R_2 \cdot \frac{k_1}{1-k_1} (3)[/itex]

[itex](2) -> R_2 = R_1 \cdot \frac{k_2}{1-k_2} (4)[/itex]

I put in (3) in (4) and get

[itex]R_2 = R_2 \cdot \frac{k_1}{1-k_1} \cdot \frac{k_2}{1-k_2} -> 1 = \frac{k_1}{1-k_1} \cdot \frac{k_2}{1-k_2}[/itex]

So i dont know how to get the values of [itex]R_1[/itex] and [itex]R_2 [/itex] as a function of [itex] k_1 [/itex] and [itex]k_2.[/itex]

The solution for this is given and is correct when I put it in the equations above and it fulfills everything but i just don't know how he has gotten it.

[itex]k_x[/itex] is a long function based on parameters that i just rebrand for simplicity.