How to get $\dfrac{s+z}{s+p} = 1 + \dfrac{z-p}{s+p}$ from block diagram?

Question

Topic is on state space and converting to How does one get the following equivalency

by only using the following Block Diagram Control system Block Diagram I believe there is a rule to do with this that I have not yet found.

Answer 1

Take

$$ \frac{s+z}{s+p}=\frac{s+z+p-p}{s+p}=\frac{(s+p)+(z-p)}{s+p}= \frac{s+p}{s+p}+ \frac{z-p}{s+p} = 1+\frac{z-p}{s+p}$$