Dividing perennials is a necessary chore. You'll want to stress the plant as little as possible, so if your perennial plant is a mass of tangled roots when you lift it, here's a method of untangling the roots that's less stressful on the plant as well as you.
Try soaking the entire root ball in a bucket of water, for a short period of time. Many of the roots will soften and float apart. You won't get them all loosened, but it can make the job a little easier on you and the plant.
This works especially well with plants like daylilies and Siberian iris, that can form thick matting clumps.

