How do you reduce this simple system diagram for the sake of doing algebraic manipulation?
The dotted node looks like it's A(s), and the node after H(s) looks like it's A(s)H(s), so A(s)H(s) - A(s) = A(s)(H(s) - 1) looks like the overall transfer function.

If you're not sure, any linear systems theory book should have a section on simplifying signal flow diagrams like this.