To carry out a complex or comprehensive search, it is usually best to search for each concept individually and then combine them together using the Advanced Search screen.
You can also use the search numbers to construct the search directly, eg (#1 AND #2) NOT #3. This can be particularly useful if you are using a complex combination and you need to use brackets to make the order clear. Alternatively, you could combine results #1 and #2 to make a new search result #4, and then combine that with search #3.
If you have combined searches, and then you use the history to edit one of the original search queries, this will affect all later combined searches based on it.