The balanced net ionic equation is
3Ag(s) + Au3+(aq) ——> Au(s) + 3Ag+(aq)
During this reaction Ag is oxidized and it act as reducing agent.
Au(NO3)3(aq) is reduced and it act as oxidizing agent.
The balance half reaction for the oxidation and reduction
For oxidation half 3Ag(s) ——> 3Ag+(aq) + 3e-
For reduction half Au3+(aq) + 3e- ——> Au(s)
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