Semileptonic decaysB→ρlνandD→ρlνand the heavy-quark symmetry

We determine the first correction in inverse powers of heavy-quark masses to the ratio of the differential decay rates of $B\to \rho e\nu$ and $D\to \rho e\nu$ at the kinematical point of zero hadronic recoil (maximum $q^2$) within the quark model. In this particular case of heavy-to-light meson transitions, the heavy-quark limit gives a definite prediction, and theoretical uncertainties should be minimal. This result is potentially important for the extraction of the Kobayashi-Maskawa element $V_{\mathrm{ub}}$ from future measurements.