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)

##### Correct Answer: Option D

##### Explanation

(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)