Sum of rationals

General Usage Performance
2

Your function doesn’t check for overflow, where most/all(?) operations on Rationals are checked:

julia> rats = [(typemax(Int64)-1)//typemax(Int64), (typemax(Int64)-2)//typemax(Int64), (typemax(Int64)-1)//typemax(Int64)]
3-element Vector{Rational{Int64}}:
 9223372036854775806//9223372036854775807
 9223372036854775805//9223372036854775807
 9223372036854775806//9223372036854775807

julia> sum(rats)
ERROR: OverflowError: 9223372036854775806 + 9223372036854775805 overflowed for type Int64
Stacktrace:
  [1] throw_overflowerr_binaryop(op::Symbol, x::Int64, y::Int64)
    @ Base.Checked ./checked.jl:155
  [2] checked_add
    @ ./checked.jl:167 [inlined]
  [3] +
    @ ./rational.jl:290 [inlined]
  [4] add_sum
    @ ./reduce.jl:27 [inlined]
  [5] _mapreduce(f::typeof(identity), op::typeof(Base.add_sum), #unused#::IndexLinear, 
...
 [14] sum(a::Vector{Rational{Int64}})
    @ Base ./reducedim.jl:994
 [15] top-level scope
    @ REPL[8]:1

julia> function rationalsum(numbers::Vector{T} where T<:Rational)
           den = lcm([x.den for x in numbers])
           nums = (x.num * div(den, x.den) for x in numbers)
           return sum(nums)//den
       end
rationalsum (generic function with 1 method)

julia> rationalsum(rats)
9223372036854775801//9223372036854775807
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