It sounds as if you may have an Autotrol control valve. If so the 3/4" is a tail piece part of the by-pass or control valve if no factory by-pass valve. Don't cut it if it is. It has a large 'ruber' gasket under the nut that connects it to the control of by-pass valve. You don't want to shorten the tail piece or burn the seal. Cut the plumbing tubing, remove the tail peice and nut and gasket and unsolder the reducer. Then use a coupler to connect the tai lpiece to your new plumbing.
Quality Water Associates