For the given reaction
"3Ag_{(s)}+Au(NO_3)_{3(aq)} \\rightarrow Au_{(s)}+3AgNO_{3(aq)}"
a balanced net ionic equation is
"3Ag_{(s)}+Au^{3+}_{(aq)} \\rightarrow Au_{(s)}+3Ag^+_{(aq)}"
During the reaction
Ag(s) is oxidized and it is the reducing agent,
Au(NO3)3(aq) is reduced and it is the oxidizing agent.
The balanced half reactions for the oxidation and reduction are following:
"3Ag_{(s)} \\rightarrow 3Ag^+_{(aq)} + 3e^-" (oxidation half-reaction)
"Au^{3+}_{(aq)}+3e^- \\rightarrow Au_{(s)}" (reduction half-reaction)
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