# Absolute minimum

Algebra Level 2

As $$x$$ and $$y$$ range over all non-zero real values, what is the minimum value of $\frac { |x+y| } { | x | + | y | }?$

Details and assumptions

The notation $$| \cdot |$$ denotes the absolute value. The function is given by $|x | = \begin{cases} x & x \geq 0 \\ -x & x < 0 \\ \end{cases}$ For example, $$|3| = 3, |-2| = 2$$.

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