How Do Block Diagram Simplifications Reflect Underlying Equations?

[princejan7]

Homework Statement

I am trying to understand the simplification between these two block diagrams

Homework Equations

The Attempt at a Solution

I understand the 2s+1/s has been moved past the summing junction, resulting in the 2s.
But I don't understand where the s/2s+1 block comes from

 

[BvU]

Central loop (third line from top) has to yield ... - 2s C(s) so for that one the the factor 2(s+1)/s has to be 'undone'.

Check what arrives from C(s) over the third line from the top by the time it's back at the right via the second line from the top.

 

[princejan7]

Central loop (third line from top) has to yield ... - 2s C(s) so for that one the the factor 2(s+1)/s has to be 'undone'.

Check what arrives from C(s) over the third line from the top by the time it's back at the right via the second line from the top.

thanks. Also, for the first diagram,on the very first run of the loop, is the signal exiting the (2s+1)/s block the same after it passes through the summing junction?

 

[BvU]

There is no first pass of the loop: it's just a diagram for the relationships.
A graphical rendering of a set of equations.