Complex sentence: After Cnut's death in 1035 the English throne fell to Harold Harefoot, Cnut's son by his first wife, while Harthacnut, his son by Emma, became King in Denmark.
Split into simpler sentences: After Cnut's death in 1035 the English throne fell to Harold Harefoot, Cnut's son by his first wife. And Harthacnut, Cnut's son by Emma, became King in Denmark.