Rationalize the denominator of \(\frac{3}{\sqrt[3]{3} + \sqrt[3]{81}}\). The answer can be written in the form of \(\frac{\sqrt[3]{A}}{B}\), where A and B are positive integers. Find the minimum possible value of A + B.
Find the minimum possible value of A + B.
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\(\frac{3}{\sqrt[3]{3} + \sqrt[3]{81}}= \frac{3}{\sqrt[3]{3} +\sqrt[3]{3}\cdot \sqrt[3]{27}}=\frac{3}{\sqrt[3]{3} (1+3)}\cdot \frac{\sqrt[3]{3}\cdot \sqrt[3]{3}}{\sqrt[3]{3}\cdot \sqrt[3]{3}} =\frac{3\cdot \sqrt[3]{9}}{4\cdot 3}=\color{blue}\frac{ \sqrt[3]{9}}{4}\)
\(A+B=9+4=13\)
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