I do not know now an easier way other that direct replacement and to expand the denominator. See FullForm of S0 to see the need rules.
Clear[a, b, c, S0]
S0 = ((b/c) + 1)/(b*(1 - 1/c))
rule = (b/c) -> a;
(Numerator[S0] /. rule)/(Expand@Denominator[S0] /. rule)
