Evaluate x frac 1 x 1 2 - x frac 1 x 1 2 - JAMB Mathematics 1993 Question
Evaluate (x + \(\frac{1}{x}\) + 1)2 - (x + \(\frac{1}{x}\) + 1)2
A
4x2
B
(\(\frac{2}{x}\) + 2)2
C
4
D
4(1 + x)
correct option: d
(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)
= (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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