KöMaL 2022 B5219

Prove that $\frac{|a+b+c|}{1+|a+b+c|}\le \frac{|a|}{1+|a|}+\frac{|b|}{1+|b|}+\frac{|c|}{1+|c|}.$ for all real numbers $a$, $b$, $c$. On what condition will equality occur?