Don't get trapped in a loop

Algebra Level 2

2axab+a+1+2bxbc+b+1+2cxca+c+1=1\Large \dfrac{\color{#D61F06}{2a}x}{\color{#20A900}{ab+a+1}}+\dfrac{\color{#3D99F6}{2b}x}{\color{#EC7300}{bc+b+1}}+\dfrac{\color{#69047E}{2c}x}{\color{#624F41}{ca+c+1}}=\color{#0C6AC7}{1}

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

Source : A book
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