Tìm giới hạn C=lim (x->3)( că (2x+3)-x)/(x^2-4x+3)

* Hướng dẫn giải

Chọn C

$\begin{array}{l}C=\underset{x\to 3}{\lim }\frac{\sqrt{2x+3}-x}{x^2-4x+3}=\underset{x\to 3}{\lim }\frac{2x +3-x^2}{(x- 3). (x- 1). (\sqrt{2x+3}+x) } \\ =\underset{x\to 3}{\lim }\frac{-(x-3)(x+1)}{(x-3)(x-1)\left(\sqrt{2x+3}+x\right)}\\ =\underset{x\to 3}{\lim }\frac{-(x+1)}{(x-1)\left(\sqrt{2x+3}+x\right)}\\ =\frac{-(3+\text{}1)}{(3-1).(\sqrt{2.3+\text{}3}+\text{}3)}=\frac{-1}{3}\end{array}$