Im doing the mages guild recomindation quest but the chorrol fingers of the mountain quest is messing up. When I give the chorrols mages guild member the book it doesnt automatically finish the the recomindation quest it just finishes fingers of the mountain so I cant advance. Is this happening to anybody else if theres anything I can download or do differently please let me know.

You will get your recommendation. Just finish the rest of the recommendations and you will be directed to the Arcane University.