Câu hỏi:
Cho biểu thức \(P = \frac{{{a^{\frac{1}{3}}}{b^{ – \frac{1}{3}}} – {a^{ – \frac{1}{3}}}{b^{\frac{1}{3}}}}}{{\sqrt[3]{{{a^2}}} – \sqrt[3]{{{b^2}}}}}\). Mệnh đề nào dưới đây đúng?
A. \(P = \frac{1}{{\sqrt[3]{{ab}}}}\).
B. \(P = \sqrt[3]{{ab}}\).
C. \(P = {\left( {ab} \right)^{\frac{2}{3}}}\).
D. \(P = – \frac{1}{{\sqrt[3]{{{{\left( {ab} \right)}^2}}}}}\).
Gợi ý câu trả lời
\(P = \frac{{{a^{\frac{1}{3}}}{b^{ – \frac{1}{3}}} – {a^{ – \frac{1}{3}}}{b^{\frac{1}{3}}}}}{{\sqrt[3]{{{a^2}}} – \sqrt[3]{{{b^2}}}}}\)\( = \frac{{\frac{{\sqrt[3]{a}}}{{\sqrt[3]{b}}} – \frac{{\sqrt[3]{b}}}{{\sqrt[3]{a}}}}}{{\sqrt[3]{{{a^2}}} – \sqrt[3]{{{b^2}}}}}\)\( = \frac{{\frac{{\sqrt[3]{{{a^2}}} – \sqrt[3]{{{b^2}}}}}{{\sqrt[3]{a}\sqrt[3]{b}}}}}{{\sqrt[3]{{{a^2}}} – \sqrt[3]{{{b^2}}}}}\)\( = \frac{{\sqrt[3]{{{a^2}}} – \sqrt[3]{{{b^2}}}}}{{\sqrt[3]{a}\sqrt[3]{b}}}.\frac{1}{{\sqrt[3]{{{a^2}}} – \sqrt[3]{{{b^2}}}}}\)\( = \frac{1}{{\sqrt[3]{a}\sqrt[3]{b}}}\)\( = \frac{1}{{\sqrt[3]{{ab}}}}\).
