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Based on density functional theory, the spontaneous separation in the mass-imbalanced Fermi-Fermi mixture is studied. The ground-state energy density functional is constructed with the effective contact interaction, with which the ground-state density profiles of the mixture are calculated under different conditions of mass-imbalance and coupling strength. The influence of mass-imbalance on the separation and the cloud size is analyzed. In addition, the system with both mass- and population-imbalance is also calculated and studied. Despite our rough treatment in the Thomas-Fermi approximation, it is hoped that the results may provide new clues to understand the nature of phase separation of a trapped ultracold gas in both theoretical and experimental researches in the future. [ABSTRACT FROM AUTHOR]