The simplified value of ( (1+1/(1+1/100) ) (1+1/(1+1/100) )- (1-1/(1+1/100) ) (1-1/(1+1/100) ))/( (1+1/(1+1/100) )+ (1-1/(1+1/100) )) is

ABC26GN1205 · Simplification

Subject: General Aptitude · Chapter: Simplification · Exam: · Marks: · Difficulty:

The simplified value of $\frac{\left(1+\frac{1}{1+\frac{1}{100}}\right)\left(1+\frac{1}{1+\frac{1}{100}}\right)-\left(1-\frac{1}{1+\frac{1}{100}}\right)\left(1-\frac{1}{1+\frac{1}{100}}\right)}{\left(1+\frac{1}{1+\frac{1}{100}}\right)+\left(1-\frac{1}{1+\frac{1}{100}}\right)}$ is

(a)100

(b)$\frac{200}{101}$

(c)200

(d)$\frac{202}{100}$

Answer

Answer (as printed): B

Explanation

Given $\exp .=\frac{a^{2}-b^{2}}{a+b}=a-b$ $$\begin{aligned} & =\left(1+\frac{1}{1+\frac{1}{100}}\right)-\left(1-\frac{1}{1+\frac{1}{100}}\right) \\ & =2 \times \frac{1}{(101 / 100)}=2 \times \frac{100}{101}=\frac{200}{101} . \end{aligned}$$

Explanation as extracted from the printed page; notation may be imperfect.

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