## College Algebra 7th Edition

$\displaystyle \frac{15}{4}$
The harmonic mean of $a$ and $b$ is: $\displaystyle \frac{1}{\frac{\frac{1}{a}+\frac{1}{b}}{2}}$ We plug in $a=3$ and $b=5$: $\displaystyle \frac{1}{\frac{\frac{1}{3}+\frac{1}{5}}{2}}$ $\displaystyle \frac{1}{\frac{\frac{5}{15}+\frac{3}{15}}{2}}$ $\displaystyle \frac{1}{\frac{\frac{8}{15}}{2}}$ $\displaystyle \frac{1}{\frac{8}{15*2}}$ $\displaystyle \frac{1}{\frac{8}{30}}$ $\displaystyle \frac{1}{\frac{4}{15}}$ $\displaystyle \frac{15}{4}$