AT-OEMO-FED1 2020 Problem 1

Let $x, y$ and $z$ be positive real numbers such that $x \geq y+z$ . Proof that $$\frac{x+y}{z} + \frac{y+z}{x} +\frac{z+x}{y} \geq 7$$ When does equality occur?

(Walther Janous)