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 answer is 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)