( Algebra )
Let a and b be the roots of the equation in R, then what is the value of a + b?

[tex]\Large \text{$ \sf \dfrac{x + \sqrt{3}}{x + \sqrt{x + \sqrt{3}}} + \dfrac{x - \sqrt{3}}{x - \sqrt{x - \sqrt{3}}} = \sqrt{x}$}[/tex]

Please demonstrate your reasoning clearly! Calculator, copy or AI resolutions will be disregarded!