I'm the deputy theory buff round here, maybe I can help out.

I'll start from the start. Now I know what inverted intervals are:

--------------------------------------
--------------------------------------
--------------------------------------
----7---------------------------------
----5---when inverted becomes---5----
--------------------------------- 5----
5th 4th

the notes are D and A and all that I've done is switched the A to an octave below for the second one.

A 5th when inverted becomes a 4th.... now add 5 + 4 together,
it equals 9!

Let's try it with somthing else...

--------------------------------------
--------------------------------------
----------2----------------------------
--------------------------------------
----------3-------to-------3------------
---------------------------5----------
6th 3rd

6 + 3 = 9!


I hope you understood. If you didn't I'll try to make a better explanation.

edit: Oh yeah I should probably say that the fact that they add up to 9 isn't useful when it comes to actually making music. It's just a nice little piece of music theory trivia.