Ensino Superior ⇒ Racionalize Tópico resolvido

[guilmarangon]

Como faço pra achar o fator racionalizante?
[tex3]\frac{1}{\sqrt[3]{4}+\sqrt[3]{3}}[/tex3]

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[tex3]\frac{1}{\sqrt[3]{4}+\sqrt[3]{3}} =\frac{1}{\sqrt[3]{4}+\sqrt[3]{3}}.\frac{(\sqrt[3]{4})^2-(\sqrt[3]{4})(\sqrt[3]{3})+(\sqrt[3]{3})^2}{(\sqrt[3]{4})^2-(\sqrt[3]{4})(\sqrt[3]{3})+(\sqrt[3]{3})^2}=\frac{(\sqrt[3]{4})^2-(\sqrt[3]{4})(\sqrt[3]{3})+(\sqrt[3]{3})^2}{(\sqrt[3]{4})^3+(\sqrt[3]{3})^3}=\boxed{\frac{(\sqrt[3]{4})^2-(\sqrt[3]{4})(\sqrt[3]{3})+(\sqrt[3]{3})^2}{7}}[/tex3]

Eu usei essa fatoração: [tex3]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex3]