document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #386780 by Theo(13342) $\"\"$ $\"About$

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5 / sqrt(x) would represent one term in the denominator that's a radical.
\n" ); document.write( "you just multiply the numerator and the denominator by sqrt(x) and you get:
\n" ); document.write( "(5 * sqrt(x)) / x
\n" ); document.write( "you don't worry about conjugates.
\n" ); document.write( "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.
\n" ); document.write( "try this link for an explanation of conjugtate.
\n" ); document.write( "it even addresses rationalizing the denominator.
\n" ); document.write( "http://en.wikipedia.org/wiki/Conjugate_%28algebra%29
\n" ); document.write( "suppse your number is now:
\n" ); document.write( "5 / (5 + sqrt(x)
\n" ); document.write( "you multiply both numerator and denominator by the conjugate to get:
\n" ); document.write( "(5 * (5 - sqrt(x))) / ((5+sqrt(x))*(5-sqrt(x)))
\n" ); document.write( "when you multiply these out:
\n" ); document.write( "(5 - sqrt(x)) * (5 + sqrt(x)) becomes 25 - x.
\n" ); document.write( "the middle terms containing - 5*sqrt(x) and + 5*sqrt(x) cancel out.
\n" ); document.write( "you are left with:
\n" ); document.write( "(5 * (5-sqrt(x))) / (25 - x)
\n" ); document.write( "The denominator has been rationalized.
\n" ); document.write( "1 term in the denominator doesn't require the use of conjugates.
\n" ); document.write( "2 terms in the denominator does.\r
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