haha I thought you meant slash chords. Those are complex chords with a different note in the bass, and there are many complex things about them that make them a serious topic of study for guitar players. This could be a little bit of fun extra research for you :)

http://www.myguitarworkshop.com/guitar_lessons/chords/guitar_slash_chords_part1.aspx

If you would like to learn "Broken Chords" then you should first learn about triads and also get a handle of the fretboard. The sooner you memorize all of the notes on the fretboard the better you will be when it comes to harmony on the guitar. I recommend studying this subject at least 15 minutes a day until you get it.

With that knowledge, you will progress much much faster than any of your peers :) there is an exercise on this site http://www.musictheory.net/exercises that specifically quizzes you on the fretboard and it will help you, but I also recommend printing or writing out a visual aid of the fretboard to study whenever you can.

once you learn about triads you will see that the quickest and fastest way to learn how to play any chord in any inversion anywhere on the neck is by memorizing the fretboard. It will take a while but the knowledge is invaluable.