SOLUTION: rationalize the denominator of: 14/((5^(1/3))-(2^(1/3)))

Question 819768: rationalize the denominator of:
14/((5^(1/3))-(2^(1/3)))
Answer by jsmallt9(3758) (Show Source): 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.)

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.

Our denominator is two terms with a "-" between them. So if we treat the as the "a" and the 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:

Before we actually multiply, let's simplify the second fraction:

Now we multiply. In the numerator we use the Distributive Property. In the denominator the pattern tells us how it works out:

which simplifies as follows:

RELATED QUESTIONS
Rationalize the denominator:... (answered by josgarithmetic)

rationalize the denominator 5 ____ sqrt 2... (answered by nyc_function,pjbcnm)

Rationalize the denominator: {{{5/(1-sqrt(3))}}} Divide... (answered by Edwin McCravy)

Simplify (Rationalize The Denominator) a)(1)/(\sqrt(5))... (answered by Boreal)

help with Rationalize the denominator squareroot of 3 -1 ________________________... (answered by edjones)

rationalize the denominator of each expression... thanks key: [ means square roots (answered by stanbon)

Rationalize the denominator.... (answered by nshah11)

Please help me to rationalize the denominator 1-squart root of 7/4+3*the square root... (answered by JBarnum)

rationalize the denominator? cube root(2/3) (answered by stanbon)