It all depends on what type of tree it is, and how long the trees been there. If it's a pine, it will have a lot of hair roots. If it is a hardwood like an Oak, it will have a long taproot, and will be a ***** to get out. Other trees like Silver Maple, Willow, Mulberry, will have long feeder roots.
The tractor you are renting, is it a skidsteer, or just like a regular tractor with a front end loader?
We took out an ornamental Weeping Mulberry that was planted at the corner of our house when we bought it. It was maybe 6' tall, 7' tall, and had a trunk about a foot or a little less in diameter. A friend I hired to do some dirt work around here, I asked him if he could pop it out. He had a 953 BobCat Skidsteer. It would not pop the tree out. we chained it up all around the trunk and limbs so the chains would not slip. He pulled, pushed, raised, lowered, and finally got it loose. The feeder roots were growing along the foundation, maybe a little larger than a golf ball in size, a half dozen roots, not counting the hair roots, and the feeders were almost 30' long.
So depending on your ground, the type of tree, the type of tractor, and the type of roots, you may have an easy time, or it bmay be a real bear.
Good luck, and pics!!!! We need pics of this undertaking.