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3r^2 - 6r - 44 = 0 - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \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:

📌 \frac{b^2(x^2 + 1)}{b^2(x^2 - 1)} + \frac{b^2(x^2 - 1)}{b^2(x^2 + 1)} = \frac{x^2 + 1}{x^2 - 1} + \frac{x^2 - 1}{x^2 + 1}

📌 Let $ y = \frac{x^2 + 1}{x^2 - 1} $, then the expression becomes:

📌 y + \frac{1}{y}

📌 We compute $ y + \frac{1}{y} $. First, recall that $ x + \frac{1}{x} = 5 $. Square both sides:

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