Complex sentence: They had met while Barenboim was still married to the British cellist Jacqueline du Pré, but by the time Barenboim met Bashkirova, du Pré had been diagnosed with multiple sclerosis.
Split into simpler sentences: They had met while Barenboim was still married to the British cellist Jacqueline du Pré. By the time Barenboim met Bashkirova, du Pré had been diagnosed with multiple sclerosis.