Limits practice question 21

A difference of two square roots sits on top. What do the top and the bottom do at $x = 2$, and how do you clear roots from a difference?

Substitution gives $\tfrac{0}{0}$. Multiply the top and the bottom by the conjugate $\sqrt{5x + 6} + \sqrt{x + 14}$.

The new numerator is $(5x + 6) - (x + 14)$. Simplify it and look for a factor of $x - 2$.