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S={(x+y−zx+y+z)2+(x−y+zx+y+z)2+(−x+y+zx+y+z)2:x,y,z∈R+}S = \left \{\left(\frac{x+y-z}{x+y+z}\right)^2 + \left(\frac{x-y+z}{x+y+z}\right)^2 + \left(\frac{-x+y+z}{x+y+z}\right)^2: x,y,z \in \mathbb R^+ \right \}S={(x+y+zx+y−z)2+(x+y+zx−y+z)2+(x+y+z−x+y+z)2:x,y,z∈R+}
Let SSS be a set defined as above, where x,y,zx, y, zx,y,z are positive real numbers.
If a=sup Sa = \text{sup } S a=sup S (((supremum of S)S)S) and b=inf Sb = \text{inf } S b=inf S (((infimum of S),S),S), compute ab\frac{a}{b}ba.
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