Complex sentence: Following her departure from "Australian Idol", Coulter was offered recording contracts by record labels including the show's parent company Sony BMG, and signed with Australia's biggest independent label Shock Records.
Split into simpler sentences: Following her departure from "Australian Idol", Coulter was offered a recording contract by several record labels, including the show's parent company Sony BMG. However, Coulter signed with Australia's biggest independent label Shock Records.