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We observe the decays of B^+-> eta pi^+ and B^+-> eta K^+; the measured branching fractions are Br(B^+-> eta pi^+) = (4.8^{+0.8}_{-0.7}(stat) +- 0.3 (sys)) * 10^-6 and Br(B^+-> eta K^+) = (2.1 +- 0.6 (stat) +- 0.2 (sys)) * 10^-6. Their corresponding CP violating asymmetries are measured to be 0.07 +- 0.15 +- 0.03 for eta pi^+- and -0.49 +- 0.31 +- 0.07 for eta K^+-. 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