jmc

We begin by multiplying out the denominator and then squaring both sides $$\begin{array}{rl}\frac{\sqrt{5x}}{\sqrt{3(x-1)}}& =2\\ (\sqrt{5x}{)}^2& ={\left(2\sqrt{3(x-1)}\right)}^2\\ 5x& =12(x-1)\\ 12& =7x\\ x& =\boxed{\frac{12}{7}}.\end{array}$$Checking, we see that this value of $x$ satisfies the original equation, so it is not an extraneous solution.