Complex sentence: When he was demobbed after seven years of military service, Cooper took up show business on Christmas Eve, 1947--he would later add a popular monologue about his military experience as "Cooper the Trooper".
Split into simpler sentences: When he was demobbed after seven years of military service Cooper took up show business on Christmas Eve, 1947. He later developed a popular monologue about his military experience as "Cooper the Trooper".