Fractions With Twists And Turns

Algebra Level 4

\[\large \displaystyle \sum_{\text {cyc}} \dfrac{a}{bc+1}\] Let \(a,b\) and \(c\) be positive reals satisfying \(a+b+c=3\).

Find the minimum value of the expression above.

Bonus: Find as many approaches as possible


This problem was taken from Hanoi grade 10 selection test for specialized students
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