Addition of inert gas to equilibrium mixture under constant pressure [duplicate]

Adding inert gas under constant volume will not disturb equilibrium. But I want to know what would happen if inert gases are added at constant pressure. If total pressure remains constant and inert gases are added, then mole fraction of any gas participating in equilibrium decreases and hence partial pressure decreases. If $\Delta n$ is non zero, then $K$ changes. But how can $K$ change if temperature remains constant?