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Problem Solving (PS) | Re: What is the equivalent expression of

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MathRevolution wrote:

[GMAT math practice question]

What is the equivalent expression of\((\frac{1}{x+y+z})(\frac{1}{x}+\frac{1}{y}+\frac{1}{z})(\frac{1}{xy+yz+zx})(\frac{1}{xy}+\frac{1}{yz}+\frac{1}{zx})\) ?

A.\(\frac{ 1}{x+y+z} \)

B.\(\frac{1}{xy+yz+zx} \)

C.\(\frac{1}{xyz}\)

D.\((\frac{1}{xyz} )^2\)

E.\(\frac{xy+yz+zx}{x+y+z}\)


\((\frac{1}{x+y+z})(\frac{1}{x}+\frac{1}{y}+\frac{1}{z})(\frac{1}{xy+yz+zx})(\frac{1}{xy}+\frac{1}{yz}+\frac{1}{zx})\)=
\((\frac{1}{x+y+z})(\frac{xy+yz+xz}{xyz})(\frac{1}{xy+yz+zx})(\frac{x+y+z}{xyz})\) =\((\frac{1}{xyz})^2\)
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