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Math·Advanced Math·Equivalent expressions

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If x > 1, which of the following is equivalent to $\frac{1}{\frac{1}{x+1}+\frac{1}{x-1}}$?

A

$\frac{x^2-1}{2x}$

B

$\frac{2x}{x^2-1}$

C

$\frac{x^2+1}{2x}$

D

$\frac{2x}{x^2+1}$