Let $a,\,b,\,c$ be positive numbers. Prove that $$\sum\limits_{cyc}\,\dfrac{a}{\sqrt{b(\,a+ b\,)}}\geqq \sum\limits_{cyc}\,\dfrac{a}{\sqrt{b(\,c+ a\,)}}$$ I tried Holder and $\lceil$ https://artofproblemsolving.com/community/c6h194103p1065812 $\rfloor$ but it's too hard to access! I need to the hint, interest from MSE-ees and hope to see $uvw$ help here! Thanks a lot!

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    $\begingroup$ At first glance, this looks to me like something for the rearrangement inequality. Have you tried applying that? $\endgroup$ – Arthur May 18 at 14:28
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    $\begingroup$ @HaiDangel If it's true it's a very interesting problem. Where did you take this inequality? $\endgroup$ – Michael Rozenberg May 19 at 6:40
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    $\begingroup$ @HaiDangel Where you took this problem? $\endgroup$ – Michael Rozenberg May 20 at 5:55

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