Remarkable Question

Algebra Level 2

\[ \large \dfrac1{a+bc} +\dfrac1{b+ac} + \dfrac1{c+ab} = \dfrac x{ \left(1 + \frac ab\right)\left(1 + \frac bc\right)\left(1 + \frac ca\right) } \]

Let \(a,b\) and \(c\) be positive real numbers satisfying \(\dfrac1a + \dfrac1b + \dfrac1c = 1\), find the value of \(x\) satisfying the algebraic identity above.

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