Fractions With Twists And Turns

Algebra Level 4

cycabc+1\large \displaystyle \sum_{\text {cyc}} \dfrac{a}{bc+1} Let a,ba,b and cc be positive reals satisfying a+b+c=3a+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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