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1. $x + \frac{1}{x} = 5$

Answer: Option D

Explanation:

x + \frac{1}{x} = 5 \Rightarrow x^{2} + 1 = 5 x .' . \frac{x}{x^{2} + x + 1} = \frac{x}{x^{2} + 1 + x} = \frac{x}{5 x + x} = \frac{x}{6 x} = \frac{1}{6}

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