SOLUTION: Rationalize the denominator or simplify {{{(1-sqrt(2))/(2sqrt(3)-sqrt(6))}}}

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Question 53617: Rationalize the denominator or simplify %281-sqrt%282%29%29%2F%282sqrt%283%29-sqrt%286%29%29
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
I gave your probelm directions and changed your expression a little to be what I see most often. If I guessed wrong,ley me know.
You need to multiply the denominator by its conjugate, so that it becomes the difference between two squares (a+b)(a-b)=a^2-b^2. What ever you multiply by the denominator also has to be multiplied by the numerator.
%281-sqrt%282%29%29%2F%282sqrt%283%29-sqrt%286%29%29

You have to foil here:


12=4*3
%282sqrt%283%29-sqrt%286%29-sqrt%284%29%2Asqrt%283%29%29%2F%2812-6%29
The square root of 4 is 2.
%282sqrt%283%29-sqrt%286%29-2sqrt%283%29%29%2F6%29
-sqrt%286%29%2F6
Happy calculating!