An algebra problem by Gurīdo Cuong

Algebra Level 4

\[\large \dfrac{\sqrt{x}}{x^2+1+2\sqrt{xy}}+\dfrac{\sqrt{y}}{y^2+1+2\sqrt{2y-xy}}+\dfrac{\sqrt{2-x}}{x^2-4x+5+2\sqrt{2x-x^2}}\]

If \(x\) and \(y\) are real numbers satisfying \(\dfrac{1}{\sqrt{x}}+\dfrac{1}{\sqrt{y}}+\dfrac{1}{\sqrt{2-x}}=3\), find the maximum value of the expression above.

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