The main result contained in this paper is described as follows. Let be a compact set in the extended complex plane , be a nonnegative integer and be continuous. Let us consider the best rational approximation of in the uniform metric on by the set of rational functions of order at most , that is, . Denote by the interior of and assume that is a compact subset with . If has nonempty connected complement, , is connected and is analytic in and nonrational, then
in particular, . Here denotes the condenser capacity associated with the condenser . The main result is derived by using the Hankel operator associated to and to an adequate family of domains , where, for every domain of , denotes its Smirnov class and is the orthogonal projection from onto .