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The approximation of |x| by rational functions is a classical rational problem. This paper deals with the rational approximation of the function x^αsgnx, which equals |x| if α = 1. We construct a Newman type operator r_n(x) and show min_|x|≤1 {|x^αsgnx − r_n(x)| } ∼ Cn^−α2 e^−2nα , where C is a constant depending on α. , number=3, journal=Communications in Mathematical Research, year=2021, month=May, pages=193–199