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RU-ALLRUSSIAN 1968 Problem 5

    Prove that:

    2/(x2−1)+4/(x2−4)+6/(x2−9)+…+20/(x2−100)=2 / (\mathrm{x}^{2} - 1) + 4 / (\mathrm{x}^{2} - 4) + 6 / (\mathrm{x}^{2} - 9) + \ldots +20 / (\mathrm{x}^{2} - 100) = 11/((x−1)(x+10))+11/((x−2)(x+9))+…+11/((x−10)(x+1)).11 / ((\mathrm{x} - 1)(\mathrm{x} + 10)) + 11 / ((\mathrm{x} - 2)(\mathrm{x} + 9)) + \ldots +11 / ((\mathrm{x} - 10)(\mathrm{x} + 1)).

    Dataset text NuminaMath olympiads. Quoted with source.

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