In this paper, we set up the general formulation to study distinguished res
idual representations of a reductive group G by the relative trace formula
approach. This approach simplifies the argument of [JR], which deals with t
his type of relative trace formula for a special symmetric pair (GL(2n), Sp
(2n)) and also works for non-symmetric, spherical pairs. To illustrate our
idea and method, we complete our relative trace formula (both the geometric
side identity and the spectral side identity) for the case (G(2), SL(3)).