Triangle Inequality

Algebra Level 4

\[E(x,y,z) = \dfrac {|x+y|}{|x|+|y|} + \dfrac {|y+z|}{|y|+|z|} + \dfrac {|z+x|}{|z|+|x|}\]

The above expression is defined for non-zero reals \(x, y, z\).

If the minimum value of \(E\) is \(a\) and the maximum value is \(b\), find \(a+b\).

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