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write an ionic and net ionic equation for the following reaction between Fe3+ and NH4OH.

ionic: Fe3+(aq) + NH4OH--> Fe(OH)3 + NH4+

net ionic: Fe3+ +OH- -->Fe(OH)3

Your ionic equation is correct. Since NH4OH is a weak electrolyte (actually it has been shown that NH4OH doesn't exist), I would write the same equation as the net ionic equation. Then if I really wanted to attract attention I would change it to write:
Fe^+3(aq) + NH3(g) + H2O(l) ==> Fe(OH)3(s) + NH4^+

NiCl2(aq) + LiOH(aq) = NiOH(s) + LiCl(aq)

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