Those stubborn roots

Algebra Level 3

x+3x+x+3+x3xx3=x\frac{x+\sqrt 3}{\sqrt x +\sqrt{x+\sqrt 3}}+\frac{x-\sqrt{3}}{\sqrt x -\sqrt{x-\sqrt3}} = \sqrt x If xx is a positive integer satisfying the above expression, find the value of xx.

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