Show that for (g) and (h) analytic functions at (z_{0}), with (gleft(z_{0} ight) eq 0, hleft(z_{0} ight)=0),

Show that for \(g\) and \(h\) analytic functions at \(z_{0}\), with \(g\left(z_{0}\right) eq 0, h\left(z_{0}\right)=0\), and \(h^{\prime}\left(z_{0}\right) eq 0\),

\[\operatorname{Res}\left[\frac{g(z)}{h(z)} ; z_{0}\right]=\frac{g\left(z_{0}\right)}{h^{\prime}\left(z_{0}\right)}\]