Ta tính
$\underset{x \to 2}{\lim} \dfrac{\sqrt{x + 2} - x}{\sqrt{4x + 1} - 3} = \underset{x \to 2}{\lim} \dfrac{ (x + 2 - x^2)(\sqrt{4x + 1} + 3)}{(4x + 1 - 9)(\sqrt{x + 2} + x)}$
$= \underset{x \to 2}{\lim} \dfrac{(2-x)(x + 1)(\sqrt{4x + 1} + 3)}{4(x-2)(\sqrt{x+2} + x)}$
$= \underset{x \to 2}{\lim} \dfrac{-(x+1)(\sqrt{4x+1} + 3)}{4(\sqrt{x + 2} + x)}$
$= \dfrac{-(2+1)(3 + 3)}{4(2 + 2)} = -\dfrac{9}{8}$