If I for example have a fraction
\begin{align} \frac{1}{(x-e) \space \ln (x)} \end{align}
can I use partial fraction decomposition to get an equation like this?
\begin{align} \frac{A}{x-e} + \frac{B}{\ln (x) }\end{align}
When I tried to do the math, I got
\begin{align} \frac{1}{x-e} + \frac{1}{(1-e) \space \ln (x)} \end{align}
which has the same form as the first equation, but it's a little wrong. I suspect I need a function $f(x)$ instead of $B$, but I don't know what that should be. I also think this might not be possible as I've only heard of partial fraction decomposition when there's polynomials involved.