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Home » R(x) = rac(x - 1)(x + 1)x + 1 - Silent Sales Machine

R(x) = rac(x - 1)(x + 1)x + 1 - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 x = z + b + a, \quad y = z + b

📌 Now express each term:

📌 \( \frac{y}{x - y} = \frac{b + z}{a} \)

📌 \( \frac{z}{y - z} = \frac{z}{b} \)

📌 \( \frac{z}{x - z} = \frac{z}{a + b} \)

📌 S = 1 + 2\left( \frac{b + z}{a} + \frac{z}{b} - \frac{z}{a + b} \right)

📌 = 1 + 2z\left( \frac{1}{a} + \frac{1}{b} - \frac{1}{a + b} \right) + 2\frac{b}{a}

📌 This still depends on \( z \). But since the original expression is homogeneous (scaling \( x, y, z \) by a constant does not change the value), we can set \( z = 1 \) without loss of generality.

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