Mathematica 12.0 gives me a result of the form
Sqrt[a b + x y z] Sqrt[-(1/(- a b - x y z))]
which obviously should simplify to 1. However, even with the assumption
Simplify[Sqrt[a b + x y z] Sqrt[-(1/(- a b - x y z))], a b + x y z > 0]
Mathematica refuses to further simplify this expression. If I set any of the five variables to one by hand (i.e. delete, for instance, all occurrences of a) then it correctly simplifies.
What is the reason for this strange behaviour and how can I get Mathematica to fully simplify square root expressions like this?