lean_workbook_plus_10232

Prove that for $a, b, c, d \in \mathbb{R}^+$, the following inequality holds:\n$\frac{1}{f(a,c)} + \frac{1}{f(b,d)} \leq \frac{2}{f(\frac{a+b}{2},\frac{c+d}{2})}$\nOr in another form:\n$\frac{ac}{a+c} + \frac{bd}{b+d} \leq \frac{(a+b)(c+d)}{a+b+c+d}$