Expand g(x) as indicated and specify the values of x for which the expansion is valid.
g(x) = (b+x)^(-1) in powers of x-a, a is not equal to -b.
Sorry, that is not right ! From where do you have b+x as well as x-a ? What are the steps that you used to obtain the above step ?
You have $\displaystyle 1/(b+x)$
Step 1 :- What do you have after making the necessary substitutions as explained by my hint? Remember that you want it as powers of x-a.
Step 2 :- How do you expand $\displaystyle 1/(1+y)$ ? In this problem,what do you have in place of y ?
Later we can discuss the validity of convergence.