_ x → 3 3x - 3 2x - 4 - 2 is equal to

Given,

$\lim_{x \to 3} \dfrac{\sqrt{3x} - 3}{\sqrt{2x - 4} - \sqrt{2}}$

On rationalization we get,

$\lim_{x \to 3} \dfrac{\left(3x - 9\right) \times \left(\sqrt{2x - 4} + \sqrt{2}\right)}{\left\{\left(2x - 4\right) - 2\right\} \times \left(\sqrt{3x} + 3\right)}$

$= \lim_{x \to 3} \dfrac{3\left(x - 3\right)}{2\left(x - 3\right)} \times \dfrac{\sqrt{2x - 4} + \sqrt{2}}{\left(\sqrt{3x} + 3\right)}$

$= \dfrac{3}{2} \times \dfrac{2\sqrt{2}}{6} = \dfrac{1}{\sqrt{2}} .$