SOLUTION: Explain the difference between rationalizing the denominator in a algebraic expression whose denominator has only one term involving a radical and one whose denominator has two ter

Question 614929: Explain the difference between rationalizing the denominator in a algebraic expression whose denominator has only one term involving a radical and one whose denominator has two terms, at least one of which involves a radical?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
5 / sqrt(x) would represent one term in the denominator that's a radical.
you just multiply the numerator and the denominator by sqrt(x) and you get:
(5 * sqrt(x)) / x
you don't worry about conjugates.
when you have 2 terms in the denominator, one of which is a radical, then you have to multiply by the conjugate of those terms to eliminate the radical in the denominator.
try this link for an explanation of conjugtate.
it even addresses rationalizing the denominator.
http://en.wikipedia.org/wiki/Conjugate_%28algebra%29
suppse your number is now:
5 / (5 + sqrt(x)
you multiply both numerator and denominator by the conjugate to get:
(5 * (5 - sqrt(x))) / ((5+sqrt(x))*(5-sqrt(x)))
when you multiply these out:
(5 - sqrt(x)) * (5 + sqrt(x)) becomes 25 - x.
the middle terms containing - 5*sqrt(x) and + 5*sqrt(x) cancel out.
you are left with:
(5 * (5-sqrt(x))) / (25 - x)
The denominator has been rationalized.
1 term in the denominator doesn't require the use of conjugates.
2 terms in the denominator does.

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