Question 851430
Hello.  Here is how you would solve your problem.


{{{-sqrt(18)/sqrt(12)}}}


First, simplify the radicals in the numerator and denominator:


{{{-sqrt(18)}}} can be reduced to {{{-3*sqrt(2)}}}


{{{sqrt(12)}}} can be reduced to {{{2*sqrt(3)}}}


Now, you are left with:


{{{(-3*sqrt(2))/(2*sqrt(3))}}}


You now have to rationalize the denominator, since you cannot have an irrational number, such as a root, in the denominator of a fraction.  To do this, we can multiply both the numerator and denominator by {{{sqrt(3)}}}.  This will eliminate the root from the denominator:


{{{(-3*sqrt(2)*sqrt(3))/(2*sqrt(3)*sqrt(3))}}}


This gives us:


{{{(-3*sqrt(6))/(2*3)}}} ----->


{{{(-3*sqrt(6))/6}}}


Finally, we can reduce the fraction down, since both the numerator and denominator of the fraction are divisible by 3.  This gives us the final answer of:


{{{-sqrt(6)/2}}}