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

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

### Question

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

### Options

A) 4x2

B) ($$\frac{2}{x}$$ + 2)2

C) 4

D) 4(1 + x)

### 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)

## Dicussion (1)

• (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)