I fixed your Latex code. Take a look so you know how to write fractions now
Oh no! You changed it back to wrong.... sigh. When writing fractions in Latex, use \frac{numerator}{denominator}
I spotted your error. You don't need to plug in s=16 and get 0 in the numerator. 16-s and s-16 are only a negative sign factored out away from equal.
$\displaystyle \frac{16-s}{(s-16)(4+sqrt(s))} = \frac{16-s}{-(16-s)(4+\sqrt{s})}$.
Now the 16-s cancels and you are left with $\displaystyle -\frac{1}{4+\sqrt{s}}$