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If x = 3+1/3-1, what is x - 1/x?

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If x = 3+1/3-1, what is x - 1/x?

by Max@Math Revolution » Tue Mar 24, 2020 12:31 am

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[GMAT math practice question]

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

A. 2
B. 2 \(\sqrt{3}\)
C. 4
D. 4 \(\sqrt{3}\)
E. 5
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Re: If x = 3+1/3-1, what is x - 1/x?

by Max@Math Revolution » Thu Mar 26, 2020 3:39 am
=>

x= √3+1/√3-1 = (√3+1)^2/(√3-1)(√3+1)=3+2√3+1/3-1=4+2√3/2=2+√3
Then x-1/x=2+√3-1/2+√3=2+√3-2-√3/(2+√3)(2-√3)=2+√3-2-√3/4-3
=2+√3-(2-√3)=2√3

Therefore, B is the answer.
Answer: B
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