Answer
$R=\frac{R_1R_2}{R_2+R_1}$.
Work Step by Step
To solve the formula for the variable $R$ means to isolate $R$ on one side of the given equation.
First we multiply both sides by $RR_1R_2$ to clear fractions.
$\Rightarrow RR_1R_2\cdot \left (\frac{1}{R}\right )=RR_1R_2\left (\frac{1}{R_1}+\frac{1}{R_2}\right )$
Use the distributive property.
$\Rightarrow R_1R_2=R\left (\frac{R_1R_2}{R_1}+\frac{R_1R_2}{R_2}\right )$
Cancel common factors.
$\Rightarrow R_1R_2=R(R_2+R_1)$
Divide both sides by $(R_2+R_1)$.
$\Rightarrow \frac{R_1R_2}{(R_2+R_1)}=\frac{R(R_2+R_1)}{(R_2+R_1)}$
Simplify.
$\Rightarrow \frac{R_1R_2}{(R_2+R_1)}=R$
$\Rightarrow R=\frac{R_1R_2}{R_2+R_1}$.
