Hi Don, yes like Steve mentions above normally you would want to trim 2 things like that with each object cutting the other.

It can be a good idea to do the trimming of things like that all in one go, which is called a "mutual trim". That's where you have some objects being trimmed where each object is both a part being cut up and also acting as a cutting object at the same time.

That looks something like this - if you start with 2 objects that are crossing through each other:



Now select both of these pieces. That will look like this:



Now run the Edit > Trim command. The trim command will see both those selected surfaces and know that those are parts that will be cut. It will then show you a prompt in the upper right area of the window that says this:



So note there that it says that you can select some cutting objects or you can push Done instead to do a mutual trim - you want to do a mutual trim in this case so instead of picking any cutting pieces you just push Done right now (or right click in a viewport which is a shortcut for pushing Done) without selecting anything else and that tells Trim to use each piece as both an object to be trimmed as well as a cutting object.

Then it will slice it up and let you pick which parts you want to discard (you can right-click on this stage instead of selecting anything if you just want to slice it up and have all the pieces). So in this case you would select these 2 fragments here:



Then when you push Done or Right-click to finish that last stage of the Trim command this will be the result:



- Michael