Olympiad Problem 6

Algebra Level 4

(ab+bc+ca)(1(a+b)2+1(b+c)2+1(c+a)2) \large (ab+bc+ca) \left (\frac 1{(a+b)^2} + \frac 1{(b+c)^2}+\frac 1{(c+a)^2} \right)

For a,b,ca, b, c are positive reals, if the infimum (minimum) value of the expression above can be expressed as xy \frac{ x}{y} for positive coprime integers xx and yy, find the value of xy x - y .

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