I've been trying to solve this limit without L'Hospital's rule because I don't know how to use derivates yet. So I tried rationalizing the denominator and numerator but it didn't work.
$$\lim\limits_{x\to 4} \frac{ \sqrt{2x+1}-3 }{ \sqrt{x-2}-\sqrt{2} }$$
By the way, the answer is supposed to be $\frac{2\sqrt{2}}{3}$.
Best Answer
Multiply top and bottom by $\sqrt{2x+1}+3$, and also by $\sqrt{x-2}+2$.