Answer
$c=\displaystyle \frac{b+3a}{2}$
Work Step by Step
The goal is to isolate the wanted variable on one side of the equation.
Neither of a,b,c can be zero, otherwise the equation is undefined.)
Add $\displaystyle \frac{3}{bc}$ to both sides
$\displaystyle \frac{1}{ac}+\frac{3}{bc}=\frac{2}{ab}\qquad$... factor out $\displaystyle \frac{1}{c}$
$\displaystyle \frac{1}{c}(\frac{1}{a}+\frac{3}{b})=\frac{2}{ab}\qquad$...multiply with $c$
$\displaystyle \frac{1}{a}+\frac{3}{b}=\frac{2c}{ab}\qquad$... multiply with $\displaystyle \frac{ab}{2}$
$\displaystyle \frac{ab}{2}\cdot\frac{1}{a}+\frac{ab}{2}\cdot\frac{3}{b}=c$
$\displaystyle \frac{b}{2}+\frac{3a}{2}=c$
$c=\displaystyle \frac{b+3a}{2}$
