Using as a tool the s-wave approximation (sWA), this work demonstrates that the nonmesonic weak decay transition rates Γn and Γp can be expressed in all hypernuclei up to 29 Λ Si (and very likely in heavier ones too) in the same way as in the s-shell hypernuclei, i.e., as a linear combination of only three elementary transition rates. This finding leads to the analytic prediction that, independently of the transition mechanism, all hypernuclei that are on the stability line (N = Z), i.e., 5 Λ He, 7 Λ Li, 9 Λ Be, 11 Λ B, 13 Λ C, 17 Λ O, 29 Λ Si, etc should roughly have the same ratio Γn/Γp, the magnitude of which rapidly increases when one approaches the neutron drip-line (N ≫ Z), and opposite happens when one goes toward the proton drip-line (N ≪ Z).