Hiring someone would mean that someone makes money off copying. This exact point is central to the way the law is set up in Denmark. It's fine to make a copy of something you own for your own private use, provided you do it yourself. The point being that no-one makes money from the copying.
It's also okay to make a so-called "analogue" copy of something you borrow, such as CD to tape or a photocopy of a book - again, provided you do it yourself. I think the law was made mostly with a view to music, because while it's easy to make a digital copy of a CD, it's quite a bit of work to convert a p-book into an e-book. The main point though - decreased quality of the copy, so as not to make a free, exact copy of the original work - is the same.
All in all, as the law is explained on the web site of the Cultural Ministry, the
intent is to not bother people if they want use things they've bought legally, in whatever way they wish. The law could be improved, but at least I feel that as long as I don't deprive someone of possible income, I am with the intent of the law, if not completely within the letter of the law. I guess this goes for many of us here
A bit more info here - through Google translator