We present a lattice quantum chromodynamics determination of the scalar and vector form factors for the B-s -\u3e D(s)l. decay over the full physical range of momentum transfer. In conjunction with future experimental data, our results will provide a new method to extract vertical bar V-cb vertical bar, which may elucidate the current tension between exclusive and inclusive determinations of this parameter. Combining the form factor results at nonzero recoil with recent HPQCD results for the B -\u3e Dl(v) form factors, we determine the ratios f(0)(Bs -\u3e Ds) (M-pi(2))/f(0)(B -\u3e D) (M-K(2))=1.000(62) and f(0)(Bs -\u3e Ds) (M-pi(2))/f(0)(B -\u3e D)(M-pi(2))=1.006(62). These results give the fragmentation fraction ratios f(s)/f(d) = 0.310(30)(stat)(21)(syst)(6)(theor)(38)(latt) and f(s)/f(d) = 0.307(16)(stat)(21)(syst)(23)(theor)(44)(latt), respectively. The fragmentation fraction ratio is an important ingredient in experimental determinations of Bs meson branching fractions at hadron colliders, in particular for the rare decay B(B-s -\u3emu(+)mu(-). In addition to the form factor results, we make the first prediction of the branching fraction ratio R(D-s) = B(B-s -\u3e D-s tau nu)/B(B-s -\u3e D-s tau nu)= 0.301(6), where l is an electron or muon. Current experimental measurements of the corresponding ratio for the semileptonic decays of B mesons disagree with Standard Model expectations at the level of nearly four standard deviations. Future experimental measurements of R(D-s) may help understand this discrepancy
