Answer
$\dfrac{15}{13} \text{ ohms}$
Work Step by Step
Extending the given formula for $3$ resistances results to $
\dfrac{1}{R}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}
.$
Using the formula above then,
\begin{array}{l}\require{cancel}
\dfrac{1}{R}=\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{2}
\\\\
30R\left(\dfrac{1}{R}\right)=\left(\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{2}\right)30R
\\\\
30(1)=6R(1)+5R(1)+15R(1)
\\\\
30=6R+5R+15R
\\\\
30=26R
\\\\
\dfrac{30}{26}=R
\\\\
R=\dfrac{15}{13}
.\end{array}
Hence, the combined resistance is $
\dfrac{15}{13} \text{ ohms}
.$
