NMC 1988 Problem 2

Let $a, b$, and $c$ be non-zero real numbers and let $a \geq b \geq c$. Prove the inequality

$$\frac{a^{3}-c^{3}}{3} \geq a b c\left(\frac{a-b}{c}+\frac{b-c}{a}\right)$$

When does equality hold?