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Home » Bob's work rate: \(\frac115\) of the task per hour - AMAZONAWS

Bob's work rate: \(\frac115\) of the task per hour - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📌 \frac{a}{b} + \frac{b}{a} = 5

📌 Let $ x = \frac{a}{b} $. Then $ \frac{b}{a} = \frac{1}{x} $, so:

📌 x + \frac{1}{x} = 5

📌 We want to compute:

📌 \frac{a^2 + b^2}{a^2 - b^2} + \frac{a^2 - b^2}{a^2 + b^2}

📌 Note that:

📌 a^2 + b^2 = b^2(x^2 + 1), \quad a^2 - b^2 = b^2(x^2 - 1)

📌 So the expression becomes:

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