Q: Is it possible to lose fat and gain muscle at the same time?

A: It is possible and common for beginners who just started following good diet and training programs. It is also possible for people who are significantly overweight. However as one makes progress with one's body composition and training, it becomes more and more difficult to lose fat and build muscle at the same time. So after the first several months I would recommend adjusting your diet to continue meet your goals effectively. That means undereating slightly to slowly lose weight and fat (1 pound per week is a good target for losing fat) OR overeating very slightly to gain weight and muscle (2 pounds a month is a good target for muscle building).