How does adding a compensator at the end of the gun reduce recoil?
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You are possibly mixing up some terminology.
A compensator helps with the reduction of muzzle rise. Muzzle rise is the tendency of a weapons muzzle to rise upwards when fired. This is because most hand-held weapons are braced below the midline of the barrel.
Recoil is the energy imparted into the weapon by firing. The direction of movement is directly opposite of the direction of the projectile. A muzzle brake helps reduce recoil.
Muzzle brakes and compensators operate on the same basic principle. They direct the flow of gas from the muzzle to create a force on the weapon being fired (similar to how rockets direct a flow of gas to push the rocket forward). A compensator will direct the gas upwards. This results in a downwards force on the muzzle that helps arrest muzzle rise. A muzzle brake redirects gas backwards toward the rear of the weapon (its also angles out to the sides to not blast the shooter with hot gas). This imparts a force on the weapon opposite of recoil.
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