1.

The value of \(1 - \frac{1}{{1 - \frac{1}{{1 - \frac{1}{x}}}}}\) is1. \(\frac{1}{x}\)2. x + 13. x4. None of the above

Answer» Correct Answer - Option 3 : x

Given:

\(1 - \frac{1}{{1 - \frac{1}{{1 - \frac{1}{x}}}}}\)

Calculations:

\(1 - \frac{1}{{1 - \frac{1}{{1 - \frac{1}{x}}}}}\)

⇒ \(1 - \frac{1}{{1 - \frac{1}{{\frac{x - 1}{x}}}}}\)

⇒ \(1 - \frac{1}{{1 - \frac{x}{{{x - 1}{}}}}}\)

⇒ \(1 - \frac{1}{{\frac{x - 1 - x}{{{x - 1 }{}}}}}\)

⇒ \(1 - \frac{x - 1}{{{ -1}{{{}}}}}\)

⇒ 1 + x - 1

⇒ x

∴ The required value of the given expression is x



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