document.write( "Question 819768: rationalize the denominator of:
\n" ); document.write( "14/((5^(1/3))-(2^(1/3))) \n" ); document.write( "
Algebra.Com's Answer #493366 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
Since 1/3 as an exponent means cube root and since radicals display better on algebra.com than fractional exponents, I am going to rewrite the expression with radicals. (Note: This is not required. All the steps below work out exactly the same with exponents of 1/3.)

\n" ); document.write( "\"14%2F%28%285%5E%281%2F3%29%29-%282%5E%281%2F3%29%29%29\"
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\n" ); document.write( "One way to look at this is that it shows use how to take two terms with a \"-\" between them, multiply it by something, and end up with an expression of nothing but perfect cubes.

\n" ); document.write( "Our denominator is two terms with a \"-\" between them. So if we treat the \"root%283%2C+5%29\" as the \"a\" and the \"root%283%2C+2%29\" as the \"b\" in the pattern, the pattern tells what what to multiply it by to get perfect cubes: . But we can't just multiply the denominator by something. We must multiply the numerator by the same thing, too:
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\n" ); document.write( "Before we actually multiply, let's simplify the second fraction:
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\n" ); document.write( "Now we multiply. In the numerator we use the Distributive Property. In the denominator the pattern tells us how it works out:
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\n" ); document.write( "which simplifies as follows:
\n" ); document.write( "\"%2814root%283%2C+25%29%2B14root%283%2C+10%29%2B14root%283%2C+4%29%29%2F%285-2%29\"
\n" ); document.write( "\"%2814root%283%2C+25%29%2B14root%283%2C+10%29%2B14root%283%2C+4%29%29%2F3\" \n" ); document.write( "
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