Let a,b,c>0 and a+b+c = 3. Prove that ((((ab)/(ab+1))+((bc)/(bc+1))+((ca)/(ca+1)))/((1/(ab+1))+(1/(bc+1))+(1/(ca+1)))) ≥ abc (Found by WolframAlpha and inspired by my old problem)


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Question Number 144742 by loveineq last updated on 28/Jun/21

$Let a, b, c > 0 and a + b + c = 3 . Prove that$ $\frac{\frac{a b}{a b + 1} + \frac{b c}{b c + 1} + \frac{c a}{c a + 1}}{\frac{1}{a b + 1} + \frac{1}{b c + 1} + \frac{1}{c a + 1}} ⩾ a b c$ $(Found by WolframAlpha and$ $inspired by my old problem)$
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