  In the context of f(R,T) theories of gravity, we study the evolution of
scalar cosmological perturbations in the metric formalism. According to
restrictions on the background evolution, a specific model within these
theories is assumed in order to guarantee the standard continuity equation.
Using a completely general procedure, we find the complete set of differential
equations for the matter density perturbations. In the case of sub-Hubble
modes, the density contrast evolution reduces to a second-order equation. We
show that for well-motivated f(R,T) Lagrangians the quasistatic approximation
yields to very different results from the ones derived in the frame of the
concordance {\Lambda}CDM model constraining severely the viability of such
theories.
