Inequality with max I want to understand

Hi,

I was reading a paper and hit an inequality I have never seen before:

(a + b) / (c + d) <= max (a/c, b/d)

In the paper I have the additional constraints that c > 0, d > 0, a >=
0, b >= 0.
I am interested in where this comes from and other examples. If there
are
books or other resources that contain stuff similar to this I would
like to know.
I have no idea how I might search for something like this online for
example.
I haven't sat down yet for an extended period to try and prove this.
I don't really have an idea of how to try and tackle it either.
Mathematica can find counter examples with negative variables but not
with the additional constraints.

Thanks.
Neill.
.

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