Multiplying both sides by $ x $:

February 22, 2026

Multiplying both sides by $ x $:

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Question: A renewable energy system’s efficiency is modeled by the equation $ \frac{a + 2b}{a - 2b} + \frac{a - 2b}{a + 2b} = 2 $. Find $ \frac{a^2 + 4b^2}{a^2 - 4b^2} $.
Solution: Let $ x = \frac{a + 2b}{a - 2b} $. Then the equation becomes:
x + \frac{1}{x} = 2
x^2 + 1 = 2x \Rightarrow x^2 - 2x + 1 = 0 \Rightarrow (x - 1)^2 = 0 \Rightarrow x = 1
So $ \frac{a + 2b}{a - 2b} = 1 \Rightarrow a + 2b = a - 2b \Rightarrow 4b = 0 \Rightarrow b = 0 $
Now compute $ \frac{a^2 + 4b^2}{a^2 - 4b^2} $. Since $ b = 0 $, this becomes:

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