Answer
$R_1 = \frac{RR_2}{R_2 - R}$
Work Step by Step
$Solve$ $the$ $equation$ $for$ $the$ $indicated$ $variable:$
$\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2};$ $for$ $R_1$
Solve for $R_1$
Subtract $\frac{1}{R_2}$ from both sides
$\frac{1}{R} - \frac{1}{R_2} = \frac{1}{R_1} + \frac{1}{R_2} - \frac{1}{R_2}$
Simplify
$\frac{1}{R} - \frac{1}{R_2} = \frac{1}{R_1}$
$\frac{1}{R_1} = \frac{1}{R} - \frac{1}{R_2}$
Combine the right side to a single fraction by finding the common denominator $(RR_2)$
$\frac{1}{R_1} = \frac{1\times R_2}{R\times R_2} - \frac{1\times R}{R_2\times R}$
$\frac{1}{R_1} = \frac{R_2 - R}{RR_2}$
Cross Multiply between both sides
$R_1 (R_2 - R) = 1 (RR_2)$
Divide both sides by $(R_2 - R)$
$\frac{R_1(R_2 - R)}{R_2 - R} = \frac{RR_2}{R_2 - R}$
$R_1 = \frac{RR_2}{R_2 - R}$
