Giới hạn của

- Hướng dẫn giải

$\begin{array}{l}\underset{x\to 2}{\lim }\frac{\sqrt{3(x+1)}-3}{x-\sqrt{x+2}}=\underset{x\to 2}{\lim }\frac{(\sqrt{3(x+1)}-3)(\sqrt{3(x+1)}+3)(x+\sqrt{x+2})}{(\sqrt{3(x+1)}+3)(x+\sqrt{x+2})(x-\sqrt{x+2})}\\ =\underset{x\to 2}{\lim }\frac{\left[3\right(x+1)-9](x+\sqrt{x+2})}{(\sqrt{3(x+1)}+3)(x^2-x-2)}=\underset{x\to 2}{\lim }\frac{(3x-6)(x+\sqrt{x+2})}{(\sqrt{3(x+1)}+3)(x+1)(x-2)}\\ =\underset{x\to 2}{\lim }\frac{3(x+\sqrt{x+2})}{(\sqrt{3(x+1)}+3)(x+1)}=\frac{2}{3}\end{array}$

Chọn đáp án B