Let \( a, b, c>0 \). Show that \[ \frac{b+c}{3 a+b+c}+\frac{a+c}{a+3 b+c}+\frac{a+b}{a+b+3 c} \geq \frac{6}{5} . \]
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Our goal is to show that the sum of three fractions is greater than or equal to \(\frac{6}{5}\). Each fraction has a similar structure, with the numerator being the sum of two variables and the denominator being the sum of all three variables with one of them Show more…
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