I just saw this article where it says you can calculate P/E using this formula. P/E = P/B / ROE

I have never seen this relationship before. Is this a correct formula?

\frac{P}{B} = \frac{P}{E} \times \frac{E}{B}

\frac{P}{B} = \frac{P}{E} \times ROE

\frac{P}{E} = \frac {\frac{P}{B}}{ROE}