The relative branching fractions of B+ -> h(+)h('+)h('-) decays, where h((')) is a pion or kaon, are measured. The analysis is performed with a data sample, collected with the LHCb detector, corresponding to an integrated luminosity of 3.0 fb(-1) of pp collisions. The results obtained improve significantly on previous measurements of these quantities, and are important for the interpretation of Dalitz plot analyses of three-body charmless hadronic decays of B+ mesons.