My number 15 tooth broke. Is it better to get an implant after the extraction or just the extraction alone?

Whenever possible, it is better to place an implant at the time of the extraction than to wait. By placing the implant immediately there is less chance that the bony ridge what time to resorb or if it's a top back to that the floor of the sinus will be allowed to drop. If too much time were allowed to lapse, then additional grafting procedures would could have been avoided will become necessary. Also, by placing the implant immediately you will reduce the risk of the neighboring teeth shifting or the opposing tooth erupting.There are a few exceptions to this rule such as if the site needs to be heavily grafted, In a case such as this, the grafted bone should be allowed to adequately heal first before the implant is placed into it.

Both options are good, it all depends on the area and condition of that tooth. If the area is ok, i suggest to have extraction, immediate setting of implant and bone graft,when you can find primary stabilityif not, just perform the extraction, and let it heal,for at least 3 months, and then you can place the implants. Hope this helps.