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)
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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)
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