Abstarct: In this thesis we used the numerical methods and with introduse Remez algoritm obtained explicitly the best polynomial approximation to functions. Then we use the Chebyshev polynomial properties and chebyshev alternation theorem and obtained explicitly the best uniform polynomial approximation to a class of rational functions. In the end we presented some theorems about the best approximation of this class of rational functions. Furthermore we obtained the alternating set of the mentioned class.