Algebra · Absolute value · Equations · Monotone functions · Subadditivity
Problem 2, 2022
Find all pairs of real numbers \((x, y)\) satisfying
\[ \frac{|x+y|}{1+|x+y|} = \frac{|x|}{1+|x|} + \frac{|y|}{1+|y|}. \]
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Serbian Municipal Competition 2022, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source