Find the value of (1+a)^2 + (a-1)^2 (1+a)^2 - (a-1)^2 for 0<a<1

Find the value of (1+a)^2 + (a-1)^2 (1+a)^2 -… | GMAT Sprint

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PS · Problem Solving

705-805

Roots

Find the value of $\frac{\sqrt{(1+a)^2} + \sqrt{(a-1)^2}}{\sqrt{(1+a)^2} - \sqrt{(a-1)^2}}$ for 0

Answer Choices

Correct answer marked below

1/a

Correct

(a-1)/(a+1)

(a+1)/(a-1)

a/(a-1)

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Explanation

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Official Explanation

Official

Note that

\sqrt{x^2}=|x|

\frac{\sqrt{(1+a)^2} + \sqrt{(a-1)^2}}{\sqrt{(1+a)^2} - \sqrt{(a-1)^2}}=\frac{|1+a|+|a-1|}{|1+a|-|a-1|}

Now, since

0<a<1

, then:

|1+a|=1+a

and

|a-1|=-(a-1)=1-a

.…

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What this question tests

What it tests

Your handling of square and higher roots, including simplifying radicals.

Common trap

Forgetting the ± when taking a square root to solve an equation, or assuming √(a²) = a.

Find the value of (1+a)2+(a−1)2(1+a)2−(a−1)2\frac{\sqrt{(1+a)^2} + \sqrt{(a-1)^2}}{\sqrt{(1+a)^2} - \sqrt{(a-1)^2}}(1+a)2​−(a−1)2​(1+a)2​+(a−1)2​​ for 0