Olympiad Problem 6

Algebra Level 4

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

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

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