How do women act carelessly and cause destruction to their peers in both Macbeth and The Great Gatsby?
Lady Macbeth causes much destruction, directly and then indirectly, in Shakespeare's Macbeth. I'm not sure I would classify her as careless, however. She is extremely deliberate when she manipulates her husband into going ahead with the assassination of Duncan. She's also deliberate in her plans and attempts to hide their guilt. If she's careless, it's in her failure to realize that once she got Macbeth started, he would order further deaths and become a tyrant, all of which turn his subjects against him and convince others that he was guilty of treachery in the killing of Duncan. But I'm not sure that could have been foreseen by Lady Macbeth.
Daisy, Jordan, and Myrtle are certainly careless in The Great Gatsby. Daisy lets Gatsby take the blame for the accident then just leaves town, even after Wilson kills Gatsby. Jordan comes right out and says that she is a careless driver, and just depends on other drivers to watch out for her. Jordan is also amoral. And Myrtle appears to not consider Wilson or any consequences when it comes to her affair with Tom. Plus, of course, she runs out in front of a moving car depending on the car to stop, which not only results in her death, but in the deaths of Wilson and Gatsby.
In short, Lady Macbeth is aggressive and deliberate when she causes destruction. The women in Gatsby are more passive and careless when their actions lead to destruction.
Lady Macbeth isn't careless at all in her manipulation of Macbeth. She knows exactly how to press his buttons and she continues to do so, knowing that he is beginning to fear for his life and everything that she wants, because it is also clear that he is not as interested in continually amassing more and more power the way his wife is.
I would point out Daisy in particular from The Great Gatsby because of her incredible ability to use whomever is convenient whether it is Tom, Gatsby, or anyone else. She has always been able to manipulate people and never cares for the consequences because her beauty will always get her out of the bad situations without consequences.