Complex sentence: By age 17, her acting skills were noticed by actor Lawrence Barrett, and earned her an invitation to appear in "The Rajah" at the Madison Square Theatre in New York, where she made her Broadway debut in 1884 and assumed her stage name.
Split into simpler sentences: By age 17, her promise as a actor was noted by actor Lawrence Barrett, and earned her an invitation to appear in "The Rajah" at the Madison Square Theatre in New York. She made her Broadway debut in 1884 and assumed her stage name.