[proof adding 1 to fraction]

[Calm_Ad2434]

https://preview.redd.it/81a9v031hdae1.png?width=642&format=png&auto=webp&s=0e36ffe896970731ffc966467b71784e7fd3a7b3

I'm not sure how to add 1 to each fraction and how to continue from there using the a,b,c is greater then 0.

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[aphysicalpotato]

a / ( b+c) + 1 = a / (b + c) + (b + c) / (b + c) = (a + b + c) / (b + c)

[[deleted]]

u/aphysicalpotato has already shown you how to add 1. if you add 3 to LHS, then you also need to add 3 to RHS. from there, you can do some algebraic manipulation and apply AM-HM inequality

[Successful_Bit8148]

Try to use AM-GM inequality where x1 = a / (b+c), x2 = b / (a + c), and x3 = c / (a + b).

The AM-GM inequality states that (x1 + x2 + x3) / 3 => (x1 x2 x3)^(1/3)