Please help with the subject and predicate of the sentence below???

despite news reports to the contrary, manufacturing jobs in the united states are expanding, which is a solid indicator of a growing economy

First, put parentheses around all prepositional and other phrases and dependent clauses (can't be sentences on their own). You should end up with this:

(Despite news reports) (to the contrary), manufacturing jobs (in the United States) are expanding (which is a solid indicator of a growing economy.)

What words are left? Now isolate the verb, the ACTION. Then tell who or what is doing that action. That's the subject.

Do you need the simple subject and simple predicate? Or do you need the complete subject and the complete predicate?