Question 634569
<pre>
{{{2sqrt(x)/(sqrt(3)-sqrt(x))}}}

We form the conjugate of the denominator which is just like it but 
we change the sign of the second term.  So the conjugate is {{{(sqrt(3)+sqrt(x))}}}.
Put that over itself, like this: {{{(sqrt(3)+sqrt(x))/(sqrt(3)+sqrt(x))}}}

Multiply by that fraction:

{{{(2sqrt(x)/(sqrt(3)-sqrt(x)))*((sqrt(3)+sqrt(x))/(sqrt(3)+sqrt(x)))}}} =  {{{2sqrt(x)/(sqrt(3)-sqrt(x))*(sqrt(3)+sqrt(x))/(sqrt(3)+sqrt(x))}}} = {{{(2sqrt(3x)+2x)/(3+sqrt(3x)-sqrt(3x)-x)}}} = {{{(2sqrt(3x)+2x)/(3-x)}}}