solve the system of equations for positive real numbers

$\displaystyle \frac{1}{xy}=\frac{x}{z}+1,\frac{1}{zy}=\frac{y}{x }+1, \frac{1}{xz}=\frac{z}{y}+1$

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- Dec 5th 2012, 08:55 AMayushdadhwalx,y,z
solve the system of equations for positive real numbers

$\displaystyle \frac{1}{xy}=\frac{x}{z}+1,\frac{1}{zy}=\frac{y}{x }+1, \frac{1}{xz}=\frac{z}{y}+1$ - Dec 5th 2012, 12:00 PMchiroRe: x,y,z
Hey ayushdadhwal.

As a hint, try getting each variable in terms of the others and then get rid of two by substituting in.

I'll wait for you to get the variables in terms of the others (like y in terms of (x,z) x in terms of (y,z) and z in terms of (x,y)).