Maximum of rational functions with same denominators

by Johnny Que   Last Updated August 13, 2019 20:20 PM - source

Suppose I have the following condition:

$$\max \left\{ \frac{x}{z},\frac{y}{z} \right\}$$ where $x,y,z$ are all non-negative (real) functions. Is it theoretically correct to state that this is equivalent to: $$\frac{\max \left\{ x,y\right\}}{z}$$ I'm having some trouble proving this. Your help is much appreciated! Thanks!

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