We consider f(R,T) theory of gravity, where R is the curvature scalar and T is the trace of the energy momentum tensor. Attention is attached to the special case, f(R,T)=R+2f(T) and two expressions are assumed for the function f(T),(a₁Tⁿ+b₁)/(a₂Tⁿ+b₂) and a₃In^q(b₃T^m), where a₁,a₂ ,b₁,b₂,n,a₃ ,b₃,q and m are input parameters. We observe that by adjusting suitably these input parameters, energy conditions can be satisfied. Moreover, an analysis of the perturbations and stabilities of de Sitter solutions and power-law solutions is performed with the use of the two models. The results show that for some values of the input parameters, for which energy conditions are satisfied, de Sitter solutions and power-law solutions may be stables.