The black fang can attack with both the bite and the 2 claws in the same turn.
#Natural Attacks: Attacks made with natural weapons, such as claws and bites, are melee attacks that can be made against any creature within your reach (usually 5 feet). These attacks are made using your full attack bonus and deal an amount of damage that depends on their type (plus your Strength modifier, as normal). You do not receive additional natural attacks for a high base attack bonus. Instead, you receive additional attack rolls for multiple limb and body parts capable of making the attack (as noted by the race or ability that grants the attacks). If you possess only one natural attack (such as a bite—two claw attacks do not qualify), you add 1–1/2 times your Strength bonus on damage rolls made with that attack.