Evaluate \((x + \frac{1}{x} + 1)^2 - (x + \frac{1}{x} + 1)^2\)

  • A \(4x^2\)
  • B \((\frac{2}{x}\) + 2)^2\)
  • C 4
  • D 4(1 + x)
jamb 1993mathematics

The correct answer is D. 4(1 + x)

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

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

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

= (2x) (2 + \(\frac{2}{x}\)) = 2x x 2(1 + \(\frac{1}{x}\))

4x (1 + \(\frac{1}{x}\)) = 4x + 4

= 4(1 + x)

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