3 - Inequalities

Let $a,b,c$ be positive real numbers such that 

$abc = 1$. 

Prove that

$\dfrac{1}{ab + a + 2} + \dfrac{1}{bc + b + 2} + \dfrac{1}{ca + c + 2} ≤ \dfrac{3}{4}$. 

Proposed by Marcel Chirita, Bucharest, Romania

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