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Home » How a Legless Lizard Survives Without Limbs—But It’s More Amazing Than You Think! - Carbonext

How a Legless Lizard Survives Without Limbs—But It’s More Amazing Than You Think! - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Instead, observe:

📌 \frac{x^2 + 1}{x^2 - 1} + \frac{x^2 - 1}{x^2 + 1} = y + \frac{1}{y} = \frac{x^2 + 1}{x^2 - 1} + \frac{x^2 - 1}{x^2 + 1}

📌 Let’s compute this directly using the identity:

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

📌 \frac{2(x^2 + 1)}{x^2 - 1}

📌 From earlier, $ x + \frac{1}{x} = 5 \Rightarrow x^2 + \frac{1}{x^2} = 23 $, so:

📌 x^2 + 1 = x^2 + \frac{x^2}{x^2} = x^2 + 1 \Rightarrow \text{Try direct substitution}

📌 Let $ x = \frac{a}{b} $, then $ x + \frac{1}{x} = 5 \Rightarrow x^2 + \frac{1}{x^2} = 23 $, so:

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