Question 48421
What is happening here is that the numerators and the denominators are being multiplied by the conjuate of the radical.  The conjugate causes the elimination of the radical.  It is the same as the difference of two squares:
{{{(a^2-b^2)}}} = (a-b)(a+b)
(a-b) is the conjugate of (a+b) and (a+b) is the conjugate of (a-b).
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a.) {{{1/(sqrt(x)+sqrt(y))=(sqrt(x)-sqrt(y))/(x-y)}}}
[Multiply the numerator and denominator by the conjugate of 
(sqrt(x)+ sqrt(y)) which is (sqrt(x)- sqrt(y))
.
1(sqrt(x)-sqrt(y)/(sqrt(x)+ sqrt(y)(sqrt(x)- sqrt(y)
When you multiply a square root by itself, the radical sign cancels out:
Example: (sqrt(3)(sqrt(3)= sqrt(9)= 3
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Cancel if possible:
1(sqrt(x)- sqrt(y)/(x)-(y)
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(sqrt(x)- sqrt(y)/x-y