Evaluate (x + 1x 1 x + 1)2 - (x + 1x 1 x + 1)2

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

Answer Details

(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)