## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$c=\displaystyle \frac{b+3a}{2}$
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 $\displaystyle \frac{ab}{2}$ $\displaystyle \frac{ab}{2}\cdot\frac{1}{a}+\frac{ab}{2}\cdot\frac{3}{b}=c$ $\displaystyle \frac{b}{2}+\frac{3a}{2}=c$ $c=\displaystyle \frac{b+3a}{2}$