How can I calculate the following limit without using l'Hôpital's rule?
$\displaystyle \lim_{x\to 2}\frac {\sqrt{x+2}-\sqrt{3x-2}}{\sqrt{4x+1}-\sqrt{5x-1}}$
The original expression is equal $\displaystyle \left( {\frac{{ - 2x + 4}}{{ - x + 2}}} \right)\left( {\frac{{\sqrt {4x + 1} + \sqrt {5x - 1} }}{{\sqrt {x + 2} + \sqrt {3x - 2} }}} \right).$