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



Dicussion (1)

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