Задание 15.11

Question

15.11. Упростите выражение $$\frac{a^{\frac{2}{3}}-2 a^{\frac{1}{3}} b^{\frac{1}{3}}+b^{\frac{2}{3}}}{a^{\frac{4}{3}}-a^{\frac{2}{3}} b^{\frac{2}{3}}}: \frac{a^{\frac{1}{3}} b^{\frac{1}{3}}-b^{\frac{2}{3}}}{a b^{\frac{1}{3}}+a^{\frac{2}{3}} b^{\frac{2}{3}}} .$$

Gimli · Accepted Answer

$$\frac{a^{\frac{2}{3}}-2 a^{\frac{1}{3}} b^{\frac{1}{3}}+b^{\frac{2}{3}}}{a^{\frac{4}{3}}-a^{\frac{2}{3}} b^{\frac{2}{3}}}: \frac{a^{\frac{1}{3}} b^{\frac{1}{3}}-b^{\frac{2}{3}}}{a b^{\frac{1}{3}}+a^{\frac{2}{3}} b^{\frac{2}{3}}}=\frac{\left(a^{\frac{1}{3}}-b^{\frac{1}{3}}\right)^{2}}{a^{\frac{2}{3}} \cdot\left(a^{\frac{2}{3}}-b^{\frac{2}{3}}\right)} \cdot \frac{a^{\frac{2}{3}} \cdot b^{\frac{1}{3}}\left(a^{\frac{1}{3}}+b^{\frac{1}{3}}\right)}{b^{\frac{1}{3}}\left(a^{\frac{1}{3}}-b^{\frac{1}{3}}\right)}=\frac{\left(a^{\frac{1}{3}}-b^{\frac{1}{3}}\right) \cdot\left(a^{\frac{1}{3}}+b^{\frac{1}{3}}\right)}{a^{\frac{2}{3}}-b^{\frac{2}{3}}}=\frac{a^{\frac{2}{3}}- b^{\frac{2}{3}}}{a^{\frac{2}{3}}-b^{\frac{2}{3}}}=1$$

Задание 15.11

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Задание 15.11

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