La Muerte De Lord Edgware/lord Edgware's Death

Poirot had been present when Jane bragged of her plan to 'get rid of' her estranged husband. Now the monstrous man was dead, but how could Jane have stabbed Lord Edgware to death in his library at exactly the same time she was seen dining with friends? And what could be her motive now that the aristocrat had vinally granted her a divorce?