When you've taken out the factor of N you're left with something like
az / (bz + c)
where z is the exponential and b & c match the denominator of N. Working back from the answer, you know you want it as a partial fraction
d + e/(bz + c)
where this can be made to match e with the numerator of N (pull out a constant).
So simply divide az by (bz+c) to express in partial fractions. You'd get
a/b + r/(bz+c)
where e=r is the (constant) remainder after (polynomial) division, i.e.
-ca/b
That's pretty much it.