Answer
$R=\frac{r_1r_2}{r_2+r_1}$
Work Step by Step
Eliminate the fractions by multiplying the LCD $Rr_1r_2$ to both sides of the equation:
$\require{cancel}
Rr_1r_2\left(\frac{1}{R}\right)=Rr_1r_2\left(\frac{1}{r_1} + \frac{1}{r_2}\right)
\\\cancel{R}r_1r_2\left(\frac{1}
{\cancel{R}}\right)=Rr_1r_2\left(\frac{1}{r_1}\right) + Rr_1r_2\left(\frac{1}{r_2}\right)
\\r_1r_2=R\cancel{r_1}r_2\left(\frac{1}{\cancel{r_1}}\right) + Rr_1\cancel{r_2}\left(\frac{1}{\cancel{r_2}}\right)
\\r_1r_2=Rr_2+Rr_1$
Factor out $R$:
$r_1r_2=R(r_2+r_1)$
Divide $(r_2+r_1)$ to both sides:
$\frac{r_1r_2}{r_2+r_1}=\frac{R(r_2+r_1)}{r_2+r_1}
\\\frac{r_1r_2}{r_2+r_1}=R$
