Excel in math, science, and engineering

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\[\frac{(z+z\sqrt{xy})^2}{(x+y)(z^2+1)}+\frac{2z}{(1+z^2)\sqrt{1+z^2}}\]

Given that \(x,y,z\) are positive reals and \(x(1-yz)=y+z\). Find the maximum value of the expression above.

Give your answer to two decimal place.

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