SOLUTION: √6/1-√3

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Question 309962: √6/1-√3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%286%29%2F%281-sqrt%283%29%29 Start with the given expression.


Multiply both the numerator and the denominator by 1%2Bsqrt%283%29


%28sqrt%286%29%2A%281%2Bsqrt%283%29%29%29%2F%281-3%29 FOIL the denominator


%28sqrt%286%29%2A%281%2Bsqrt%283%29%29%29%2F%28-2%29 Combine like terms.


%28sqrt%286%29%2Bsqrt%286%29%2Asqrt%283%29%29%2F%28-2%29 Distribute.


%28sqrt%286%29%2Bsqrt%286%2A3%29%29%2F%28-2%29 Combine the last two roots.


%28sqrt%286%29%2Bsqrt%2818%29%29%2F%28-2%29 Multiply


%28sqrt%286%29%2Bsqrt%289%2A2%29%29%2F%28-2%29 Rewrite 18 as 9*2


%28sqrt%286%29%2Bsqrt%289%29%2Asqrt%282%29%29%2F%28-2%29 Break up the second root.


%28sqrt%286%29%2B3%2Asqrt%282%29%29%2F%28-2%29 Take the square root of 9 to get 3.


-%28sqrt%286%29%2B3%2Asqrt%282%29%29%2F%282%29 Factor out a negative 1.


%28-sqrt%286%29-3%2Asqrt%282%29%29%2F%282%29 Distribute that negative 1 through the numerator.


So sqrt%286%29%2F%281-sqrt%283%29%29=%28-sqrt%286%29-3%2Asqrt%282%29%29%2F%282%29