I’m not sure Symbolics.jl is really setup for this kind of work but maybe @ChrisRackauckas or @cryptic.ax can comment on that. You can do a similar trick as Symbolics.jl simplify exp(0) to 1 - #2 by langestefan
julia> using Symbolics
julia> a = sqrt(Num(3))
sqrt(3)
julia> rules = RuleSet([@rule(~x / ~s => ~x * ~s / (~s)^2)])
SymbolicUtils.Rewriters.Walk
julia> simplify(a - 3/a, rewriter=rules)
0
Which works because this rule is built in:
julia> sqrt(Num(3))^2
3