Show that the $\max{ \{ x,y \} }= \frac{x+y+|x-y|}{2}$. Show that the $\max{ \{ x,y \} }= \dfrac{x+y+|x-y|}{2}$. 
I do not understand how to go about completing this problem or even where to start.

For another approach we can do as follows:
$$max(x, y) - max(-x, -y) = x + y$$
and,
$$max(x, y) + max(-x, -y) = |x - y|$$
Adding those together yeilds:
$$2\times max(x, y) = x + y + |x - y|$$
Dividing by two, gives us what we want.
