Answer
$\displaystyle \frac{15}{4}$
Work Step by Step
The reciprocals of 3 and 5 are $\displaystyle \frac{1}{3}$ and $\displaystyle \frac{1}{5}$
Their average is $\displaystyle \frac{\frac{1}{3}+\frac{1}{5}}{2}=\frac{\frac{5+3}{15}}{\frac{2}{1}}=\frac{8\cdot 1}{15\cdot 2}=\frac{4}{15}$
The reciprocal of the average (the harmonic mean) is
$\displaystyle \frac{15}{4}$
