SOLUTION: how do you solve {{{-12/sqrt(18x)}}}? I have gotten to {{{-12sqrt( 2*9*x )/(18x)}}} but am unsure of what to do with the numbers under the radicand

Don't start out multiplying by the entire denominator over itself.
Instead, first get the prime factorization of 18 as 2*3²



To get a perfect square under the radical,
we need to multiply what's under there by another 2 and also
by another x, so we multiply by  which is just 1 in value.



Multiplying under the radicals in the denominator:



Now we will no longer have a radical in the
denominator because we can take the square roots
of all those squares





Then the 6 divides into the 12 and we have:



Edwin