Question

Скоротити дріб

$\frac{{x}^{ \frac{1}{3} } + \sqrt[6]{x \times y} }{ \sqrt[6]{x \times y} + {y}^{ \frac{1}{3} } }$
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Answer 1

$\displaystyle\bf\\\frac{x^{\dfrac{1}{3} } +\sqrt[6]{xy} }{\sqrt[6]{xy} +y^{\dfrac{1}{3} } } =\frac{\Big(x^{\dfrac{1}{6}} \Big)^{2} +x^{\dfrac{1}{6} } \cdot y^{\dfrac{1}{6} } }{x^{\dfrac{1}{6} } \cdot y^{\dfrac{1}{6} }+\Big(y^{\dfrac{1}{6} }\Big)^{2} } =\frac{x^{\dfrac{1}{6}} \cdot\Big(x^{\dfrac{1}{6} } + y^{\dfrac{1}{6} }\Big) }{y^{\dfrac{1}{6} } \cdot \Big(x^{\dfrac{1}{6} }+ y^{\dfrac{1}{6} }\Big) } =\\\\\\=\frac{x^{\dfrac{1}{6} } }{y^{\dfrac{1}{6} } }$