Answer
$-13$
Work Step by Step
Recall that if $ f $ is a polynomial function, then we have $\lim_\limits{x\to a}f(x)=f(a)$.
In order to to find the limit, we will plug $ a $ into the function and then simplify.
$\lim_\limits{x\to 9} \dfrac{\sqrt x+10}{\sqrt x-10}=\dfrac{\lim_\limits{x\to 9} \sqrt x+10}{\lim_\limits{x\to 10} x-10}$
or, $=\dfrac{13}{-1}$
or, $=-13$
