After reading some more about whether it is possible to lose fat and build muscle at the same time, the answer is a QUALIFIED YES. As long as you are trying to reduce your overall body weight. So, if you are fat to begin with then this can happen.
BUT, it is much harder, if not impossible to BULK UP and LOSE FAT at the same time.
Why? Because in order to bulk up you need to consume more calories than you use. Now, if you are following a proper a diet almost all of those calories should be converted to muscle. Even so, there might be a slight gain in fat during the bulk up process.
So, first go through the bulk up and pack on the muscles. Then AFTER you are done the bulk up, go through a cutting process. Whereby you, are dropping your calorie intake to less than your daily requirement. But, at the same time you are keeping your protein intake high and maintaining the intensity of your weight routine. This will help to burn off the bat. It is also recommended to do some high intensity intermittent training in between weight routines to help the fat burning process. But, this should only be done in the cutting phase.