Question 78
Let $a$, $b$, $c$, $d$ be positive real numbers. Prove the inequality
$$
\frac{a-b}{b+c}+\frac{b-c}{c+d}+\frac{c-d}{d+a}+\frac{d-a}{a+b} \geq 0
$$
and determine all cases in which equality holds.
$$
\frac{a-b}{b+c}+\frac{b-c}{c+d}+\frac{c-d}{d+a}+\frac{d-a}{a+b} \geq 0
$$
and determine all cases in which equality holds.