Solution
= Solution
With the same factors, if $n\leq m$, then
$$
\frac{f(z)}{g(z)}=(z-a)^{m-n}\frac{F(z)}{G(z)}
$$
has no negative power and extends holomorphically across $a$. Thus its apparent singularity is a <removable singularity>, with extension value
$$
\boxed{\left(\frac fg\right)(a)=\begin{cases}F(a)/G(a),&m=n,\\0,&m>n.\end{cases}}
$$
For $m>n$ the extended quotient has a <order of a zero of a holomorphic function>[zero] of order $m-n$; for $m=n$ the extension is nonzero.