From a question in my textbook
Suppose that the transform associated with a discrete random variable X has the form $$M(s)=\frac{A(e^s)}{B(e^s)}$$ where $A(t)$ and $B(t)$ are polynomials of the generic variable t. Assume that $A(t)$ and $B(t)$ have no common roots and that the degree of $A(t)$ is smaller than the degree of $B(t)$. Assume also that $B(t)$ has distinct, real, and nonzero roots that have absolute value greater than 1. Then it can be seen that $M(s)$ can be written in the form $$M(s)=\frac{a_1}{1-r_1e^s}+\dots+\frac{a_m}{1-r_me^s}$$ where $\frac{1}{r_1}\dots\frac{1}{r_m}$ are the roots of $B(t)$ and the $a_i$ are constants that are equal to $\lim_{e^s\to \frac{1}{r_i}}(1-r_ie^s)M(s)$$,i=1,\dots, m$
I need an explanation of the whole "it can be seen that" part which was entire glossed over in my text.