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I believe you should always use the net ionic equation for finding equilibrium constants since the species that appear on both sides of the equation do not change/participate in the reaction. If you do not use the net ionic equation, the species that appear on both sides should still cancel each other out when you use the formula for K.
You should use a net ionic equation when a reaction involves fully dissociated ionic compounds in solution. A net ionic equation automatically gets rid of spectator ions, which are ions that exist in the same form in both reactant and product sides of the chemical reaction (thus, concentrations of spectator ions cancel when calculating the equilibrium constant).
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