SOLUTION: Rationalize: square root of "a" divided by the square root of "a" - 2

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Question 139600: Rationalize: square root of "a" divided by the square root of "a" - 2
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Not sure whether you mean sqrt%28a%29%2F%28sqrt%28a%29-2%29 or sqrt%28a%29%2F%28sqrt%28a-2%29%29 Either way, 'rationalize' means 'rationalize the denominator' and that means 'get that nasty radical out of my denominator'


sqrt%28a%29%2F%28sqrt%28a%29-2%29

You need to multiply the denominator by its conjugate, namely sqrt%28a%29%2B2, therefore you need to multiply the entire fraction by 1 in the form of %28sqrt%28a%29%2B2%29%2F%28sqrt%28a%29%2B2%29

%28sqrt%28a%29%2F%28sqrt%28a%29-2%29%29%28%28sqrt%28a%29%2B2%29%2F%28sqrt%28a%29%2B2%29%29

The denominator becomes the difference of two squares, and you just distribute for the numerator:

%28a-2sqrt%28a%29%29%2F%28a-4%29


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sqrt%28a%29%2F%28sqrt%28a-2%29%29

Again, you need to multiply by 1, this time in the form of sqrt%28a-2%29%2Fsqrt%28a-2%29, so:

%28sqrt%28a%29%2F%28sqrt%28a-2%29%29%29%28sqrt%28a-2%29%2Fsqrt%28a-2%29%29

%28sqrt%28a%29sqrt%28a-2%29%29%2F%28a-2%29

%28sqrt%28a%5E2-2a%29%29%2F%28a-2%29