Complex sentence: Huston remained busy throughout the 1930s and 1940s, both on stage and screen (becoming one of America's most distinguished actors); he performed "September Song" in the original Broadway production of "Knickerbocker Holiday" in 1938.
Split into simpler sentences: Huston remained busy throughout the 1930s and 1940s, both on stage and screen (becoming one of America's most distinguished actors). He performed "September Song" in the original Broadway production of "Knickerbocker Holiday" in 1938.