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GQ2
SNot a very good solution but sort of case working for the signs in x,y,z gives if x and z have signs alike and y has a different sign, then one fraction of the expression becomes 1 while the minimum value of the rest of the thing is 0.
S$\frac{\abs{\abs{x}-\abs{y}}}{\abs{x+y}}+\frac{\abs{\abs{y}-\abs{z}}}{\abs{y+z}}+\boxed{\frac{\abs{x}+\abs{z}}{\abs{x+z}}}$. The first 2 have mimimum value 0 while the last portion has value 1 in this case
TSirLancelotDuLac
