Math Problem Statement
Let a,b,c be positive real numbers such that a+b+c=1 prove that (a-bc)/(a+bc)+(b-ca)/(b+ca)+(c-ab)/(c+ab)<3/2
Solution
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Math Problem Analysis
Mathematical Concepts
Inequalities
Algebraic Manipulation
Symmetric Functions
Formulas
\(\frac{a - bc}{a + bc}\)
\(\frac{b - ca}{b + ca}\)
\(\frac{c - ab}{c + ab}\)
Theorems
Arithmetic Mean-Harmonic Mean (AM-HM) Inequality
Suitable Grade Level
Undergraduate Math (Advanced High School/College Level)