diff --git a/base/broadcast.jl b/base/broadcast.jl
index d5daab992390c..971727768a4be 100644
--- a/base/broadcast.jl
+++ b/base/broadcast.jl
@@ -941,8 +941,8 @@ broadcast_unalias(::Nothing, src) = src
 preprocess(dest, x) = extrude(broadcast_unalias(dest, x))
 
 @inline preprocess_args(dest, args::Tuple) = (preprocess(dest, args[1]), preprocess_args(dest, tail(args))...)
-preprocess_args(dest, args::Tuple{Any}) = (preprocess(dest, args[1]),)
-preprocess_args(dest, args::Tuple{}) = ()
+@inline preprocess_args(dest, args::Tuple{Any}) = (preprocess(dest, args[1]),)
+@inline preprocess_args(dest, args::Tuple{}) = ()
 
 # Specialize this method if all you want to do is specialize on typeof(dest)
 @inline function copyto!(dest::AbstractArray, bc::Broadcasted{Nothing})
diff --git a/test/broadcast.jl b/test/broadcast.jl
index 38950dd10b5b0..1cad14de44c5f 100644
--- a/test/broadcast.jl
+++ b/test/broadcast.jl
@@ -1058,3 +1058,13 @@ end
     @test println.(buf, [1,2,3]) == [nothing, nothing, nothing]
     @test String(take!(buf)) == "1\n2\n3\n"
 end
+
+@testset "Memory allocation inconsistency in broadcasting #41565" begin
+    function test(y)
+        y .= 0 .- y ./ (y.^2) # extra allocation
+        return y
+    end
+    arr = rand(1000)
+    @allocated test(arr)
+    @test (@allocated test(arr)) == 0
+end