A high-statistics sample of photoproduced charm from the FOCUS experiment has been used to search for direct CP violation in the decay rates for D+-->K(S)pi+ and D+-->K(S)K+. We have measured the following asymmetry parameters relative to D+-->K-pi+pi+: A(CP)(K(S)pi+) = (-1.6+/-1.5+/-0.9)%, A(CP)(K(S)K+) = (+6.9+/-6.0+/-1.5)%, and A(CP)(K(S)K+) = (+7.1+/-6.1+/-1.2)% relative to D+-->K(S)pi+. We have also measured the relative branching ratios and found Gamma(D+-->K(0)pi+)/Gamma(D+-->K-pi+pi+) = (30.60+/-0.46+/-0.32)%, Gamma(D+-->K(0)K+)/Gamma(D+-->K-pi+pi+) = (6.04+/-0.35+/-0.30)%, and Gamma(D+-->K(0)K+)/Gamma(D+-->K(0)pi+) = (19.96+/-1.19+/-0.96)%.