SOLUTION: If x = sqrt 3 + sqrt 2 over sqrt 3 - sqrt 2 and y=1, then the value of x-y over x-3y is ----------- ---?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: If x = sqrt 3 + sqrt 2 over sqrt 3 - sqrt 2 and y=1, then the value of x-y over x-3y is ----------- ---?      Log On


   

Question 934870: If x = sqrt 3 + sqrt 2 over sqrt 3 - sqrt 2 and y=1, then the value of x-y over
x-3y is ---------------?
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
x%22%22=%22%22%28sqrt%283%29%2Bsqrt%282%29%29%2F%28sqrt%283%29-sqrt%282%29%29, y=1

Rationalize the denominator:

x%22%22=%22%22%28sqrt%283%29%2Bsqrt%282%29%29%2F%28sqrt%283%29-sqrt%282%29%29%22%22%2A%22%22%28sqrt%283%29%2Bsqrt%282%29%29%2F%28sqrt%283%29%2Bsqrt%282%29%29 %22%22=%22%22 %283%2B2sqrt%286%29%2B2%29%2F%283-2%29 %22%22=%22%22 %285%2B2sqrt%286%29%29%2F1 %22%22=%22%22 5%2B2sqrt%286%29

%28x-y%29%2F%28x-3y%29%22%22=%22%22%28%285%2B2sqrt%286%29%29-1%29%2F%28%285%2B2sqrt%286%29%29-3%281%29%29%22%22=%22%22%285%2B2sqrt%286%29-1%29%2F%285%2B2sqrt%286%29-3%29%22%22=%22%22%284%2B2sqrt%286%29%29%2F%282%2B2sqrt%286%29%29%22%22=%22%22%282%282%2Bsqrt%286%29%29%29%2F%282%281%2Bsqrt%286%29%29%29%22%22=%22%22
%28cross%282%29%282%2Bsqrt%286%29%29%29%2F%28cross%282%29%281%2Bsqrt%286%29%29%29%22%22=%22%22%282%2Bsqrt%286%29%29%2F%281%2Bsqrt%286%29%29

Rationalize the denominator:

%282%2Bsqrt%286%29%29%2F%281%2Bsqrt%286%29%29%22%22%2A%22%22%281-sqrt%286%29%29%2F%281-sqrt%286%29%29 %22%22=%22%22 %282-sqrt%286%29-6%29%2F%281-6%29%22=%22%22%28-4-sqrt%286%29%29%2F%28-5%29%22%22=%22%22

Multiply top and bottom by -1

%284%2Bsqrt%286%29%29%2F5

Edwin