Measurement of the ratios of branching fractions B(B(s)(0)-> D(s)(-)pi(+))/B(B(0)-> D(-)pi(+)) and B(B(+)->(D)over-bar(0)pi(+))/B(B(0)-> D(-)pi(+))

We report an observation of the decay B(s)(0)-> D(s)(-)pi(+) in p (p) over bar collisions at root s = 1.96 TeV using 115 pb(-1) of data collected by the CDF II detector at the Fermilab Tevatron. We observe 83 +/- 11(stat) B(s)(0)-> D(s)(-)pi(+) candidates, representing a large increase in statistics over previous measurements and the first observation of this decay at a p (p) over bar collider. We present the first measurement of the relative branching fraction B(B(s)(0)-> D(s)(-)pi(+))/B(B(0)-> D(-)pi(+))=1.32 +/- 0.18(stat)+/- 0.38(syst). We also measure B(B(+)->(D) over bar (0)pi(+))/B(B(0)-> D(-)pi(+))=1.97 +/- 0.10(stat)+/- 0.21(syst), which is consistent with previous measurements.