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The following branching fractions have been measured: B(tau- -> K- eta nu)=(1.58 +- 0.05 +- 0.09)x 10^{-4}, B(tau- -> K- pi0 eta nu)=(4.6 +- 1.1 +- 0.4)x 10^{-5}, B(tau- -> pi- pi0 eta nu)=(1.35 +- 0.03 +- 0.07)x 10^{-3}, B(tau- -> pi- KS eta nu)=(4.4 +- 0.7 +- 0.2)x 10^{-5}, and B(tau- -> K^{*-} eta nu)=(1.34 +- 0.12 +- 0.09)x 10^{-4}. These results are substantially more precise than previous measurements. 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