Let R is a principal ideal domain(PID) and D is a multiplicatively closed subset of R.Then prove that the RING OF FRACTIONS OF D WITH RESPECT TO R(D INVERSE R) is a PID.

How to do the sum?

I have proved it when D=R-0. When D is so, the ring of fractions has a field structure.And a field is a euclidean domain, & hence a PID.

But how to prove this for any subset D?