# Three Variables, One Equation!

Algebra Level 5

$\large{x+y+z+ \dfrac3{x-1} + \dfrac3{y-1} +\dfrac3{z-1} = 2 \left( \sqrt{x+2} + \sqrt{y+2} + \sqrt{z+2} \right)}$

If the sum of all real numbers $$x,y,z \geq 1$$ satisfying the above equality can be expressed as:

$\dfrac{A}{B} \left(C+\sqrt{D}\right)$

where $$A,B,C,D$$ are positive integers, with $$\gcd(A,B)=1$$ and $$D$$ has no square factors, find the value of $$A+B+C+D$$?

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