Expand the function 3x / (x ^ 2 + 5x + 6) into a power series of X. can we put forward 3x and then multiply it

Expand the function 3x / (x ^ 2 + 5x + 6) into a power series of X. can we put forward 3x and then multiply it

That's what we should do
First of all:
1/(x+2)(x+3)=1/(x+2)-1/(x+3)
Separately
Then multiply by 3x