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

Assessment: JAMB UTME - Mathematics - 1993 Subject: General Mathematics

Question 1 Report

4x2

(

\frac{2}{x}

+ 2)2

4

4(1 + x)

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)