Using the factorization approach, we investigate the B¯0→K¯0K+π- and B¯0→K0K-π+ decays individually including the resonant and nonresonant contributions. Under the flavor SU(3) symmetry, we obtain the total branching fraction BR[B¯0→(K¯0K+π-+K0K-π+)]=(7.17-0.53-1.42-0.07+0.50+1.97+0.08)×10-6, which is in agreement with the recent measurements of BABAR and LHCb within errors. For the decay B¯0→K¯0K+π-, the nonresonant background and a0+(1450) pole in the current-induced process provide a large contribution, the latter of which has not been included in previous studies. On the contrary, the decay B¯0→K0K-π+ is dominated by the nonresonant background and the off-shell ρ- pole. When the flavor SU(3) symmetry breaking and the final-state rescattering are considered under two different scenarios, the results can also accommodate the experimental data with large uncertainties. Moreover, the direct CP asymmetry of B¯0→K¯0K+π- is found to be sensitive to the matrix element of scalar density. These predictions could be further tested in the LHCb experiment or Super-b factory in the future.