If vegetables and fruits are important sources of essential dietary nutrients, how do carnivores live healthily without them?

They can make some: Good question. One of the main nutrients that we need from fruits and vegetables is Vitamin C but almost every animal except humans, great apes and guinea pigs can manufacture Vit. C and thus don't need it in their diet. Carnivores have evolved to only require the nutrients found in meats. See https://www.truecarnivores.com/obligate-carnivores-natures-true-carnivores/