A single . can be used as the partner of a bracket, e.g.:
\left| \frac{b}{c} \right.
\left. \frac{b}{c} \right|
There is also \middle in order to scale something in the middle of an expression, e.g.:
\left. a * b = c \middle| :b \right.
However, in your case, probably you should use some way to align your computation across several lines. This can be done using, for example, the environment align from package amsmath:
\begin{align}
a * b &= c &&| :b\\
a &= \frac{c}{b}
\end{align}
This will, however, lead to the problem that you cannot use \left and \right across different cells of an align, as explained at https://tex.stackexchange.com/a/89621/88939.
$ a * b = \left. c \right| :b [and so on]. – Onner Irotsab Nov 11 '15 at 16:05