Perennial Weeds

I've been trying to get rid of ground elder since it appeared in a border 2 years ago. I find it difficult to dig up by hand, the stems break easily so it's hard to follow them back to the main root. It's the only thing I use weed killer on. It's definitely weakening, another year and I think it'll be gone, but then there wasn't that much of it in the first place and I caught it early. If it's already well established in a mixed border I can see it being impossible to get rid of.