ta có : \(\dfrac{lim}{x\rightarrow3}\dfrac{x\left(x-3\right)}{x-\sqrt{x+1}-1}=\dfrac{lim}{x\rightarrow3}\dfrac{\left(x^2-3x\right)\left(x-1+\sqrt{x+1}\right)}{\left(x-1-\sqrt{x+1}\right)\left(x-1+\sqrt{x+1}\right)}\)
\(=\dfrac{lim}{x\rightarrow3}\dfrac{\left(x^2-3x\right)\left(x-1+\sqrt{x+1}\right)}{\left(x-1\right)^2-\left(\sqrt{x+1}\right)^2}=\dfrac{lim}{x\rightarrow3}\dfrac{\left(x^2-3x\right)\left(x-1+\sqrt{x+1}\right)}{x^2-2x+1-x-1}\)
\(=\dfrac{lim}{x\rightarrow3}\dfrac{\left(x^2-3x\right)\left(x-1+\sqrt{x+1}\right)}{x^2-3x}=\dfrac{lim}{x\rightarrow3}\dfrac{x-1+\sqrt{x+1}}{ }=4\)
