How to fix White Triangles / Gaps Left between Vector Objects after Live Trace / Expand in Adobe Illustrator

Ive spent hours and described this issue in Adobe Illustrator Ive asked in every way imaginable and cannot for the life of my even find anyone else asking this question. I can't be the only one experiencing this issue. I only have about 8 hours into this program. well about 14 if you count the time spent trying to answer this question. I am very new to Illustrator but I uploaded a fairly simple image to learn on. I selected my Image / Live Trace / Expand. I experimented with many different presets, mostly 16 bit and High fidelity and I m left with a vectorized image but with several gaps between objects. some are hairline and others are triangular. I don't know why I cannot find the answer no matter how many ways I ask. I can't even find anyone asking a similar question. PLEASE HELP Ive included in images below

Thanks in advance              Matt