This might be more of a trig question, so if it is would someone kindly move it for me?

So I'm finding the second derivative of $\displaystyle ln[sec(x)+tan(x)]$. My first derivative is $\displaystyle \frac{sec(x)tan(x)+sec^2(x)}{sec(x)+tan(x)}$.

My question is: can I simplify this fraction to make taking the second derivative less tedious? I'm capable of doing it without simplifying first, but I don't want to get a super long and ugly answer.