We investigated analytically and numerically the occurrence of modulation instability in fibers with periodic changes both in dispersion and gain. Previously, it has been known that the modulation instability is suppressed in dispersion managed solitons where dispersion is managed in such a way that the local dispersion alternates between the normal and the anomalous regimes. In this work, we enhanced the advantage of the dispersion management scheme by additionally introducing proper gain/loss profiles in fibers. The gain/loss profile is given by Γ(z)=0.5/<i>D</i>(z)*(<i>dD/dz</i>), where <i>D</i>(z) represents the dispersion profile. The fundamental gain spectrum of the modulation instability in the dispersion and gain managed fibers have been derived analytically and confirmed by numerical calculation. Our investigation reveals that in the dispersion and gain fibers the modulation instabilities are always much more suppressed compared to the case that only dispersion managed. In practical dispersion management schemes, dispersion profiles show discontinuity, and thus, the corresponding gain/loss profiles tend to finite. In these cases, the gain/loss profiles were approximated by lumped gains/losses of finite values. Our numerical calculations confirm that this approximation also works well.