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ab^2 (1/(a + c)^2 +1/(a- c)^2 ) = (a -b)

Source: 1975 Hungary - Kürschák Competition p1

October 15, 2022
algebra

Problem Statement

Transform the equation ab2(1(a+c)2+1(a−c)2)=(a−b)ab^2 \left(\frac{1}{(a + c)^2} +\frac{1}{(a- c)^2} \right) = (a -b) into a simpler form, given that a>c≥0a > c \ge 0, b>0b > 0.
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