Brainsteem Mathematics Challenges: Fractions

Question

Let pq be a 2-digit decimal number, for example, if p=3 and q=1 then the number is 31.

Find the possible values of a, b and c, such that

ab/ba = bc/cb

and the fractions are not equal to 1.

As always, these questions are designed to be done by hand, without computational assistance. In this case, you should find some structure to the puzzle so that you can then generate many other such triangles of primes.

The first correct answer and further interesting comments will be rewarded with an upvote.

Enjoy!