Absolutely, but please be aware that there is a reason we undergo as much training as we do. We are able to identify issues that may arise. Its also worth considering that a shop rented machine may not have been sanitised between visits so you could be cross contaminating your carpet with the previous users dog wee, blood, or worse!
Shop rented machines also tend to not be as powerful as our machinery, so if you do hire a machine, make sure you give as much attention to the drying as you do to the actual clean itself. Opening windows is a must, and if possible try to do this on a warm day.
The product that is generally supplied with these machines is a general cleaner. We advise that you try and match your problem to the bottle of cleaner that is supplied.
Hiring a machine from shops will generally not remove issues of dog urine odours as this may already be deeper rooted in the carpet. Sometimes, carpet needs to be pulled up and underlay to be replaced.