Answer
$R_1=18.0\;\Omega$
Work Step by Step
The given values are
$R=12.0\;\Omega$ and $R_2=36.0\;\Omega$
The given formula is
$\Rightarrow \frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}$
Substitute all the values.
$\Rightarrow \frac{1}{12.0\;\Omega}=\frac{1}{R_1}+\frac{1}{36.0\;\Omega}$
Subtract $\frac{1}{36.0\;\Omega}$ from both sides.
$\Rightarrow \frac{1}{12.0\;\Omega}-\frac{1}{36.0\;\Omega}=\frac{1}{R_1}+\frac{1}{36.0\;\Omega}-\frac{1}{36.0\;\Omega}$
Simplify.
$\Rightarrow \frac{1}{12.0\;\Omega}-\frac{1}{36.0\;\Omega}=\frac{1}{R_1}$
$\Rightarrow \frac{3}{36.0\;\Omega}-\frac{1}{36.0\;\Omega}=\frac{1}{R_1}$
$\Rightarrow \frac{3-1}{36.0\;\Omega}=\frac{1}{R_1}$
$\Rightarrow \frac{2}{36.0\;\Omega}=\frac{1}{R_1}$
$\Rightarrow \frac{1}{18.0\;\Omega}=\frac{1}{R_1}$
Reciprocal both sides.
$\Rightarrow 18.0\;\Omega=R_1$.
