Chebyshev's alternance in the approximation of constants by simple partial fractions

Uniform approximation of real constants by simple partial fractions on a closed interval of the real axis is studied. It is proved that a simple partial fraction of best approximation of degree $n$ for a constant is unique and coincides with this constant at $n$ nodes lying on the interval; moreover, there is a Chebyshev alternance consisting of $n+1$ points.