Complex sentence: The American 82nd Airborne Division would land in support of the Seventh Army, while the British 1st Airborne Division conducted brigade-sized landings along the eastern coast to support the Eighth Army.
Split into simpler sentences: The American 82nd Airborne Division, would land in support of the Seventh Army. While the British 1st Airborne Division conducted brigade-sized landings along the eastern coast to support the Eighth Army.