Did the Spinosaurus live in the same place as the Trex?

No Spinosaurus and T-Rex did not live in the same place.

There have only ever been 6 specimens of Spinosaurus found to date. They have all been found in different locations in North Africa (Morocco, Egypt, Kenya, Libya and Niger)

All specimens of T-Rex have been found in the Western Part of North America. Some other Tyrannosaur species have also been discovered in Canada and Alberta.

Also although both lived in the late Cretaceous they were separated by some 25 million years. Spinosaurus lived much earlier than T-Rex. Spinosaurs lived from 97 million years ago compaired to T-Rex which lived 66,000,000 years ago.