It is shown that exactly the same results of the memory function theory of diffusion-influenced reactions, presented by Yang, Lee, and Shin, can be derived from the nonequilibrium reduced distribution function (RDF) theory. Instead of the usual dynamic superposition approximation (SA), which has been widely used to truncate the hierarchy of RDF evolution equations, we introduce another type of truncation approximation. The new approximation provides simple analytic solutions that are in better agreement with the computer simulation and the known exact results than those obtained with the SA.