Obtain the Taylor series expansion of the following function?

Questions
1

I need to taylor expand the function x^(-a-1)(1+Ax^3)^(-1)(1+Bx)^(y-1) up to order one in x, but when i use the Series “command” it expand only the third term up to first order and cancel the second one giving so a much lower order of expansion because of the first term. How can I solve this? For the expansion can be considered y>a

2

Please provide the code you used (in plain text, not as an image).

3

Series[D^(-a - 1)(1 + bD^3)^(-1)(1 + Dc)^(y - 1), {D, 0, 1}]

4

Series[D^(-a - 1)(1 + bD^3)^(-1)(1 + Dc)^(y - 1), {D, 0, 1}]

5

It is not clear to me what result is expected. Is this variant better?

Series[dd^(-a - 1) (1 + b*dd^3)^(-1) (1 + dd*c)^(y - 1), {dd, 0, 1}] // Together

(* Out[430]= dd^-a (SeriesData[dd, 0, {1, c (-1 + y)}, -1, 1, 1]) *)