Having trouble with this question:
Let f be analytic at a point w
Define
Show that g has a removable singularity at w.
Please help!
Yes, exactly; show that the numerator is zero at , and its derivative also.
The idea is that these zeroes will cancel the zeroes of the denominator - if you only had a simple zero or no zero at all at , you'd end up with a simple or a double pole there.