Rationalize the denominator of \(\displaystyle \frac{1}{\sqrt[3]{3} - \sqrt[3]{2}}\) . With your answer in the form \(\displaystyle \frac{\sqrt[3]{A} + \sqrt[3]{B} + \sqrt[3]{C}}{D}\), and the fraction in lowest terms, what is \(A + B + C + D\)?
(a^3 + b^3) = (a + b)(a^2 - ab + b^2)
==> 1/(cbrt(3) - cbrt(2)) = (6^(1/3) + 8^(1/3) + 9^(1/3))/2, so A + B + C + D = 25
