Evaluate limit without L'hopital $$\lim_{x\to2}\dfrac{\sqrt{x^2+1}-\sqrt{2x+1}}{\sqrt{x^3-x^2}-\sqrt{x+2}}$$
Please help me evaluate this limit. I have tried rationalising it but it just can't work, I keep ending up with $0$ at the denominator... Thanks!

$$\displaystyle \lim_{x\rightarrow 2}\frac{\sqrt{x^2+1}-\sqrt{2x+1}}{\sqrt{x^3-x^2}-\sqrt{x+2}}\times \frac{\sqrt{x^2+1}+\sqrt{2x+1}}{\sqrt{x^2+1}+\sqrt{2x+1}}\times \frac{\sqrt{x^3-x^2}+\sqrt{x+2}}{\sqrt{x^3-x^2}+\sqrt{x+2}}$$
So we get $$\displaystyle \lim_{x\rightarrow 2}\left[\frac{x^2-2x}{x^3-x^2-x-2}\times \frac{\sqrt{x^3-x^2}+\sqrt{x+2}}{\sqrt{x^2+1}+\sqrt{2x+1}}\right]$$
So we get $$\displaystyle \lim_{x\rightarrow 2}\frac{x(x-2)}{(x-2)\cdot (x^2+x+1)}\times \lim_{x\rightarrow 2} \frac{\sqrt{x^3-x^2}+\sqrt{x+2}}{\sqrt{x^2+1}+\sqrt{2x+1}}$$
So we get $$\displaystyle = \frac{2}{7}\times \frac{4}{2\sqrt{5}} = \frac{4}{7\sqrt{5}}$$
