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If x = 13, what is 1+x1-x - 1-x1+x ?

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If x = 13, what is 1+x1-x - 1-x1+x ?

by Max@Math Revolution » Wed Feb 26, 2020 12:47 am

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[GMAT math practice question]

If \(x=\frac{1}{\sqrt{3}}\) , what is \(\sqrt{\frac{1+x}{1-x}}-\sqrt{\frac{1-x}{1+x}}\) ?

A. 1
B. \(\sqrt{2}\)
C. 2
D. \(\sqrt{3}\)
E. 3
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Re: If x = 13, what is 1+x1-x - 1-x1+x ?

by Max@Math Revolution » Fri Feb 28, 2020 1:44 am
=>
\(\sqrt{\frac{1+x}{1-x}}-\sqrt{\frac{1-x}{1+x}}\)
\(=\sqrt{\frac{1+x}{1-x}}-\sqrt{\frac{1-x}{1+x}}\)
\(=\frac{\left(\sqrt{1+x}\right)^2-\left(\sqrt{1-x}\right)^2}{\sqrt{1-x}\sqrt{1+x}}\)
\(=\frac{\left(1+x\right)-\left(1-x\right)}{\sqrt{1-x}^2}\)
\(=\frac{2x}{\sqrt{1-x}^2}\)
\(=\frac{\frac{2}{\sqrt{3}}}{\sqrt{1-\frac{1}{3}}}=\frac{\frac{2}{\sqrt{3}}}{\frac{\sqrt{2}}{\sqrt{3}}}=\frac{2}{\sqrt{2}}=\sqrt{2}\)
Therefore, B is the answer.
Answer: B
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