Mastering Laplace Transforms: Solving Algebraic Equations with Ease

[smk037]

I put this in this forum because its actually a laplace transform question

basically, I just can't see how he is factoring out (kp)/(kp-1)
any ideas?
http://img4.imageshack.us/img4/1462/38846579.jpg

 

[Mark44]

It looks to me like a partial fractions decomposition, rewriting
$$\frac{k_p}{s(s - 1 + k_p)}~=~k_p\left(\frac{A}{s} + \frac{B}{s - 1 + k_p}\right)$$

The idea is to solve for A and B so that this equation is an identity.