In computing an asymptotic expansion I have come across the term: $$\frac{a+bx^2\log(x)}{c-\log(x)+dx^2\log(x)},$$ where $a,b,c$ and $d$ are non zero constants, in general.
I am unsure if to proceed to expand, using the geometric series expansion $$\frac{1}{1+\frac{1}{\log(x)}}=1-\frac{1}{\log(x)}+\frac{1}{\log(x)^2}-\frac{1}{\log(x)^3}+\dots$$ or leave this term as is!
I guess in essence I'm asking if $\frac{\log(x)}{\log(x)+1}$ is a 'better' form than $1-\frac{1}{\log(x)}+\frac{1}{\log(x)^2}-\frac{1}{\log(x)^3}+\dots$.
Thanks in advance!