Answer
$R=\dfrac{R_1R_2}{R_2+R_1}$
Work Step by Step
Using the properties of equality, in terms of $
R
,$ the given equation, $
\dfrac{1}{R}=\dfrac{1}{R_1}+\dfrac{1}{R_2}
,$ is equivalent to
\begin{array}{l}
RR_1R_2\left( \dfrac{1}{R} \right)=\left( \dfrac{1}{R_1}+\dfrac{1}{R_2} \right)RR_1R_2
\\\\
R_1R_2=RR_2+RR_1
\\\\
R_1R_2=R(R_2+R_1)
\\\\
\dfrac{R_1R_2}{R_2+R_1}=R
\\\\
R=\dfrac{R_1R_2}{R_2+R_1}
.\end{array}
