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We present a study of B--->D(0)(CP)K- decays, where D(0)(CP) is reconstructed in CP-even channels, based on a sample of 88.8 x 10(6) Upsilon(4S)-->BB decays collected with the BABAR detector at the PEP-II e(+)e(-) storage ring. We measure the ratio of Cabibbo-suppressed to Cabibbo-favored branching fractions B(B--->D(0)(CP)K-)/B(B--->D(0)(CP)pi(-))=[8.8+/-1.6(stat)+/-0.5(syst)]x10(-2) and the CP asymmetry A(CP)=0.07+/-0.17(stat)+/-0.06(syst). We also measure B(B--->D0K-)/B(B--->D0pi(-))=[8.31+/-0.35(stat)+/-0.20(syst)]x10(-2) using a sample of 61.0 x 10(6) BB pairs.
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