  We present a combined measurement of Rb = \Gamma(Z -> bb) / \Gamma(Z
->hadrons) and the semileptonic branching ratio of b quarks in Z decays, BR(b->
l nu X), using double-tag methods. Two analyses are performed on one million
hadronic Z decays collected in 1994 and 1995. The first analysis exploits the
capabilities of the silicon microvertex detector. The tagging of b-events is
based on the large impact parameter of tracks from weak b-decays with respect
to the e+e- collision point. In the second analysis, a high-pt lepton tag is
used to enhance the b-component in the sample and its momentum spectrum is used
to constrain the model dependent uncertainties in the semileptonic b-decay. The
analyses are combined in order to provide precise determinations of Rb and
BR(b-> l nu X):
  Rb = 0.2174 +/- 0.0015 (stat.) +/- 0.0028 (sys.);
  BR(b-> l nu X) = (10.16 +/- 0.13 (stat.) +/- 0.30 (sys.)) %.
