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Question Number 195232 by CrispyXYZ last updated on 28/Jul/23

a, b, c>0,  a+b+c≥1. Find  max Σ_(cyc)  ((a−bc)/(a+bc)).

$${a},\:{b},\:{c}>\mathrm{0},\:\:{a}+{b}+{c}\geqslant\mathrm{1}.\:\mathrm{Find} \\ $$$$\mathrm{max}\:\underset{\mathrm{cyc}} {\sum}\:\frac{{a}−{bc}}{{a}+{bc}}. \\ $$

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