Solution 3 (e).

See text and/or instructor's solution manual.

Answer.      has removable a singularity at the origin, and a simple pole at  -1.

Solution.   Write   

We know that    has a removable singularity at  ,

which implies that  that    has a removable singularity at  

Now apply  Corollary 7.5 to conclude that   has a simple pole at  -1.

Therefore,    has removable a singularity at the origin, and a simple pole at  -1.  

We are  done.   

Aside.  We can let Mathematica double check our work.

We are really done.   

          The removable a singularity at the origin, and a simple pole at  -1.  

                              A plot for   .  

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell