Quotients of continuous convex functions on nonreflexive Banach spaces

On each nonreflexive Banach space X there exists a positive continuous convex function ƒ such that 1/ƒ is not a d.c. function (i.e., a difference of two continuous convex functions). This result together with known ones implies that X is reflexive if and only if each everywhere defined quotient of two continuous convex functions is a d.c. function. Our construction also gives a stronger version of Klee's result concerning renormings of nonreflexive spaces and non-norm-attaining functionals.