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We report on new measurements of Cabibbo-suppressed semileptonic D+s decays using 3.19 fb−1 of e+e− annihilation data sample collected at a center-of-mass energy of 4.178~GeV with the BESIII detector at the BEPCII collider. Our results include branching fractions B(D+s→K0e+νe)=(3.25±0.38(stat.)±0.16(syst.))×10−3 and B(D+s→K∗0e+νe)=(2.37±0.26(stat.)±0.20(syst.))×10−3 which are much improved relative to previous measurements, and the first measurements of the hadronic form-factor parameters for these decays. For D+s→K0e+νe, we obtain f+(0)=0.720±0.084(stat.)±0.013(syst.), and for D+s→K∗0e+νe, we find form-factor ratios rV=V(0)/A1(0)=1.67±0.34(stat.)±0.16(syst.) and r2=A2(0)/A1(0)=0.77±0.28(stat.)±0.07(syst.).