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Home » The All-New Gear 5: Fixing Gears 1–4 AND Delivering Epic Performance! - Carbonext

The All-New Gear 5: Fixing Gears 1–4 AND Delivering Epic Performance! - Carbonext

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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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)}...
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} =...
x^2 + 2 + \frac{1}{x^2} = 25 \Rightarrow x^2 + \frac{1}{x^2} = 23
Now compute $ x^2 + 1 $ and $ x^2 - 1 $:
Let $ A = x^2 + 1 $, $ B = x^2 - 1 $. Then:
\frac{A}{B} + \frac{B}{A} = \frac{(x^2 + 1)^2 + (x^2 - 1)^2}{(x^2 - 1)...
Compute numerator:

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