Triangle Inequality

Algebra Level 4

E(x,y,z)=x+yx+y+y+zy+z+z+xz+xE(x,y,z) = \dfrac {|x+y|}{|x|+|y|} + \dfrac {|y+z|}{|y|+|z|} + \dfrac {|z+x|}{|z|+|x|}

The above expression is defined for non-zero reals x,y,zx, y, z.

If the minimum value of EE is aa and the maximum value is bb, find a+ba+b.

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