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Home » Alternatively, recall the formula for sum of divisors with \( a \geq 1 \): - Get link 4share

Alternatively, recall the formula for sum of divisors with \( a \geq 1 \): - Get link 4share

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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\frac{x + y}{x - y} + \frac{y + z}{y - z} + \frac{z + x}{z - x}
given that \( x > y > z \).
We are to minimize the expression
S = \frac{x + y}{x - y} + \frac{y + z}{y - z} + \frac{z + x}{z - x}
under the condition \( x > y > z > 0 \). Note that all denominators ar...
We analyze the structure of each term. Consider the identity:
\frac{x + y}{x - y} = \frac{(x - y) + 2y}{x - y} = 1 + \frac{2y}{x - y...
\frac{y + z}{y - z} = 1 + \frac{2z}{y - z}, \quad \frac{z + x}{z - x}...
Adding the three:
S = \left(1 + \frac{2y}{x - y}\right) + \left(1 + \frac{2z}{y - z}\rig...

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