I have a function $f(x) = (a+2b)\dfrac{1}{x^4} + \left[\dfrac{a}{(x-a)}\right]^4 + \dfrac{1}{x}$.
I am required to find the coefficient of the lowest power of $x$ in $f(x)$.
Is it just $(a+2b)$? Or should I account for the $\left[\dfrac{a}{(x-a)}\right]^4$ term as well?
I'm asking because I can write this term as: $$ \left[\frac{a}{(x-a)}\right]^4 = \left[\frac{a}{(x-a)} + \frac{x-x}{(x-a)} \right]^4= \left[\frac{x}{(x-a)} -1\right]^4, $$ which seems to suggest that this term "carries no power". I know this may be a very elementary question but I can't find an answer to this so any help would be really appreciated.