There are so many different possible explanations for what you're describing that it wouldn't be wise to even hazard a guess as to the cause of the blood and loose stools you're seeing from your dog.
The age and breed of your dog would be a good place to start. Are there any other problems you've noticed? Has your dog been seen by a veterinarian recently for this or any other problem? Does your dog get any table food or can it get into your trash cans? Is there any vomiting? Does your dog have access to any poisons around the house, garage, or outdoors?
Intestinal parasites (worms) would probably be your best hope for a relatively easy solution. Any of the common intestinal parasites can cause what you're describing. Next most likely would be something your dog ate that it shouldn't have...such as table food, bones, garbage, etc. Then, you get into the less common, more involved disorders that could require more testing and possibly X-rays.
Persistent blood in the stools is not something you should let go or try to treat on your own at home. A diagnosis is imperative.
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