Cho giới hạn lim x tiến tới 3 (x+1-căn 5x+1)/x-căn(4x-3)=a/b (phân số

* Hướng dẫn giải

Đáp án là C

$$\begin{gathered} \underset{x\to 3}{lim}\frac{x+1-\sqrt{5x+1}}{x-\sqrt{4x-3}} \\ =\underset{x\to 3}{lim}\frac{\left(x+1-\sqrt{5x+1}\right)\left(x-\sqrt{4x-3}\right)}{x^2-4x+3} \\ =\underset{x\to 3}{lim}\frac{\left({\left(x+1\right)}^2-5x-1\right)\left(x-\sqrt{4x-3}\right)}{\left(x^2-4x+3\right)\left(x+1+\sqrt{5x+1}\right)} \\ =\underset{x\to 3}{lim}\frac{x\left(x-3\right)\left(x-\sqrt{4x-3}\right)}{\left(x-1\right)\left(x-3\right)\left(x+1+\sqrt{5x+1}\right)} \\ =\underset{x\to 3}{lim}\frac{x\left(x+\sqrt{4x-3}\right)}{\left(x-1\right)\left(x+1+\sqrt{5x+1}\right)} \\ =\frac{9}{8} \\ Vậy T = 2a-b=10 \end{gathered}$$