Consider partial maps ∑* → $\mathbb R$
with a rationaldomain. We show that two families of such series are actually thesame: the unambiguous rational series on the one hand, and the max-plus and min-plus rational series on the other hand.The decidability of equality was known to hold in both families withdifferent proofs, so the above unifies the picture. We give an effective procedure to build an unambiguous automaton froma max-plus automaton and a min-plus one that recognize the same series.