How would I prove this inequality?

Question

$$ \text{ If }x > y > z,\text{ then }xy +yz > \frac{(x + y)(y+z)}{2} $$ All numbers $x$, $y$ and $z$ are real numbers.

Answer 1

hint

$$x>y>z\implies (x-y)(y-z)>0$$

Answer 2

Guide:

1. clear denominator

2. then subtract right side from the left side