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∑cycabc+1\large \displaystyle \sum_{\text {cyc}} \dfrac{a}{bc+1}cyc∑bc+1a Let a,ba,ba,b and ccc be positive reals satisfying a+b+c=3a+b+c=3a+b+c=3.
Find the minimum value of the expression above.
Bonus: Find as many approaches as possible
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