<s>[INST] Show that if a,b,c,d are positive then $\frac{ab}{a+b}+\frac{cd}{c+d}\le \frac{(a+c)(b+d)}{a+b+c+d}$ Show that if a,b,c,d are positive then
$\frac{ab}{a+b}+\frac{cd}{c+d}\le \frac{(a+c)(b+d)}{a+b+c+d}$
I am stuck with this.
Thanks in advance!
 [/INST] Hints: $\times (a+b)(c+d)(a+b+c+d)$ on the left side and right side.
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