"Why did not you do sth" is not grammatically wrong, but just sounds weird, instead you should say "why didn't you do sth". "Why did you not do sth" to me is the exact the same as the previous one, however when you say it, you put the emphasis on the NOT part.

It's the grammar of a question. "You did not run after a taxi" as a question becomes "why did you not run...?"

第一个:你为什么不......,表示建议，惋惜或其他的感叹. 例如:why don't you go shopping?去逛街怎么样？建议去逛街． why do you not 你为什么不.....希望对方就ＷＨＹ（为什么）　作出回答．　例如:why do you not go shopping? 你为什么不去逛街？（你可以告诉我你不去逛街的原因吗？） 两个的区别在于侧重点不同，第一个是祈使句（you)，有祈使或建议的意思，第二个是个否定式特殊疑问句． There are same with : why aren't you able to why are you not able to 这两句和上面解释是一样的． 第一句是对对方无能为力做某事而感到惋惜．建议　例如：why aren't you able to go shopping? 你去逛街吗？（反正你也没别的事） 第二句是问对方为什么不能去逛街，侧重点在希望对方就问题作出回答．例如：why are you not able to go shopping?你为什么不能去逛街呢？（是不是家里出了什么事情？）