#### Answer

\[x=\frac{ab}{c}\].

#### Work Step by Step

Simplify the provided expression as follows:
\[\begin{align}
& \frac{x+a}{a}=\frac{b+c}{c} \\
& \frac{x}{a}+\frac{a}{a}=\frac{b}{c}+\frac{c}{c} \\
& \frac{x}{a}+1=\frac{b}{c}+1
\end{align}\]
This can be further simplified as follows:
\[\begin{align}
& \frac{x}{a}=\frac{b}{c}+1-1 \\
& \frac{x}{a}=\frac{b}{c} \\
& x=\frac{ab}{c}
\end{align}\]
The solution for the provide proportion is \[x=\frac{ab}{c}\].