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Home » Hugo Spritz Hacks You Need to Try—This Recipe Is Pure Summer Magic! - Crankk.io

Hugo Spritz Hacks You Need to Try—This Recipe Is Pure Summer Magic! - Crankk.io

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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

📌 We now try a substitution to simplify. Let \( a = x - y > 0 \), \( b = y - z > 0 \), so \( x - z = a + b > 0 \). Then:

📌 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)

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