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# Rationalize the denominator of . After formatting your answer in the form , and simplifying the fraction down to its lowest terms,

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Rationalize the denominator of $$\displaystyle \frac{1}{\sqrt[3]{3} - \sqrt[3]{2}}$$. After formatting your answer in the form $$\displaystyle \frac{\sqrt[3]{A} + \sqrt[3]{B} + \sqrt[3]{C}}{D}$$, and simplifying the fraction down to its lowest terms, what is $$A + B + C + D$$?

Apr 8, 2020

#1
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See if this helps.

Apr 8, 2020
#2
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You'll need to combind conjugates with rationalizing a cube root.

HELPMEEEEEEEEEEEEE  Apr 8, 2020
#3
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You can use this identity:  a3 - b3  =  (a - b)(a2 + a·b + b2)

In this case:  a = cubr(3)  and  b = cubr(2)

So:  multiply the numerator and denominator by:  cubr(32) + cubr(3·2) + cubr(22}  =  cubr(9) + cubr(6) + cubr(4)

The numerator becomes:  cubr(9) + cubr(6) + cubr(4)

while the denominator becomes 3 - 2  =  1

A + B + C + D  =  cubr(9) + cubr(6) + cubr(4) + 1

Apr 8, 2020