Question

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Answer 1

$\displaystyle\bf\\\frac{x-y}{x^{\frac{3}{4} } +x^{\frac{1}{2} } y^{\frac{1}{4} } } \cdot\frac{x^{\frac{1}{2} } y^{\frac{1}{4} }+x^{\frac{1}{4} }y^{\frac{1}{2} }}{x^{\frac{1}{2} } + y^{\frac{1}{2} } } \cdot\frac{x^{\frac{1}{4} }y^{-\frac{1}{4} }}{x^{\frac{1}{2} } -2x^{\frac{1}{4} } y^{\frac{1}{4} }+y^{\frac{1}{2} } } =$

$\displaystyle\bf\\=\frac{(x^{\frac{1}{2} } -y^{\frac{1}{2} } )(x^{\frac{1}{2} }+y^{\frac{1}{2} } ) }{x^{\frac{1}{2} } (x^{\frac{1}{4} } +y^{\frac{1}{4} }) } \cdot\frac{x^{\frac{1}{4} } y^{\frac{1}{4} }(x^{\frac{1}{4} }+y^{\frac{1}{4} })}{x^{\frac{1}{2} } + y^{\frac{1}{2} } } \cdot\frac{x^{\frac{1}{4} }}{(x^{\frac{1}{4} } - y^{\frac{1}{4} })^{2} \cdot y^{\frac{1}{4} } } =$

$\displaystyle\bf\\\frac{(x^{\frac{1}{2} } -y^{\frac{1}{2} })\cdot y^{\frac{1}{4} }}{x^{\frac{1}{4} } } \cdot\frac{x^{\frac{1}{4} } }{(x^{\frac{1}{4} }-y^{\frac{1}{4} })^{2} \cdot y^{\frac{1}{4} } } =\frac{(x^{\frac{1}{4} }-y^{\frac{1}{4} } )(x^{\frac{1}{4} }+ y^{\frac{1}{4} } )}{(x^{\frac{1}{4} } -y^{\frac{1}{4} } )^{2} } =\\\\\\=\frac{x^{\frac{1}{4} }+x^{\frac{1}{4} }}{x^{\frac{1}{4} } -y^{\frac{1}{4} } }$