system
Given the following post, respond as if you're commenting on Reddit:
human
[Nolan Batman films] "I won't kill you, but I don't have to save you"...why does Batman kill Ra's but let Joker live?

Something bugged me while rewatching the trilogy. Batman had no problems not saving Ra's, who probably did more for Bruce becoming Batman then any other baddie ever did. Hell Ra's saved his life even.

So why does Batman save the Joker? Joker killed Rachel, turned Harvey against Gotham, tried to blow up a hospital etc. and somehow after all that Batman still saw it fit to save him from the fall. Why? I'm just trying to understand why Ra's had to die but Joker had to be "brought to justice".
gpt
The only reason Joker’s life was in danger was because Batman knocked him off the building. Batman would have been directly caused his death. 

However, Ra’s life was in danger because Batman needed to stop the train. His death was only indirectly caused by him. Had Ra’s been anywhere else he would have lived.