Don't get trapped in a loop

Algebra Level 2

\[\Large \dfrac{\color{red}{2a}x}{\color{green}{ab+a+1}}+\dfrac{\color{blue}{2b}x}{\color{orange}{bc+b+1}}+\dfrac{\color{purple}{2c}x}{\color{brown}{ca+c+1}}=\color{darkblue}{1}\]

If there are distinct positive numbers \(a,b,c\) such that \(abc=1\) and they satisfy the above equation , Find the value of \(x\).

Source : A book
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