I agree with what the others have said, and here are some reasons.
1. Your max tow rating does not include aftermarket accessories, passengers, or cargo. When you add these things to your tow vehicle, it adds weight and decreases both, your available payload and your towing capacity, pound for pound.
2. In many cases, the dry weight on a trailer does not include dealer installed options, propane, or a battery. The trailer will be heavier before it gets off the dealer lot.  Same goes for dry hitch weight.
3. The weight of hitch equipment (weight distributing hitch and anti sway bars) and the real world hitch weight from the trailer are both counted as cargo weight in the tow vehicle. SUV's are not known for being strong in the payload department.
4. As you're loading up vehicle and trailer, the gross weight of the trailer is racing up towards the tow capacity of the tow vehicle and the tow vehicle's capacity is racing down towards the gross trailer weight. In your case, you don't have much room for those numbers to move without exceeding one or more ratings.
Here's a link to a calculator that will help in your search.