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[tex]\frac{|a-b|}{1+|a|+|b|} \leq \frac{|a-c|}{1+|a|+|c|}+\frac{|c-b|}{1+|c|+|b|}, \forall a, b, c \in \mathbb{R}.[/tex]

I tried to get this from

[tex]|a-b| \leq |a-c|+|c-b|, \forall a, b, c \in \mathbb{R},[/tex]

but I couldn't succeed.

Thank you.