Why hasn't the U.S. invaded North Korea?

For one thing the US, due to it's involvement in Afghanistan, does not have the military manpower to deploy in sufficient numbers to invade North Korea by conventional means even if isted by S.Korea's forces. Therefore, it is possible the only way to take out N. Korea would be by a nuclear attack, the international result of which cannot be accurately forecast. Most certainly there would be a retaliatory strike on the US mainland by China which would, in turn, lead to everybody capable of doing so nuking anyone they have had in their sights for years - Israel/Iran being just one example. The whole mess would lead to world anarchy amongst the few surviving nations and it would be more than likely that mankind would cease to exist. Over the years I, personally, have been more than happy with the nuclear powers as the fear of atomic conflict had managed to keep us from WW3. I lived through WW2 and that was bad enough. These days with international instability on the rise I am of the opinion we are on the verge of something similar to that which I have described here. Good luck everybody!