Question

упростите выражение)))))

Answer 1

$(frac{2}{x^{frac{1}{4}}-y^{frac{1}{4}}}+frac{2}{x^{frac{1}{4}}+y^{frac{1}{4}}}) *(frac{x^{-0.5}-y^{-0.5}}{6x^{-0.25}*y^{-0.5}}) = \\ (frac{2(x^{0.25}+y^{0.25})+2(x^{0.25}-y^{0.25})}{x^{0.5}-y^{0.5}})(frac{x^{-0.5}-y^{-0.5}}{6x^{-0.25}*y^{-0.5}})= \\ frac{2*2*x^{0.25}}{x^{0.5}-y^{0.5}}(frac{frac{y^{0.5}-x^{0.5}}{x^{0.5}*y^{0.5}}}{frac{6}{x^{0.25}}*frac{1}{y^{0.5}}}) =$
$frac{2*2*x^{0.25}}{x^{0.5}-y^{0.5}}*(frac{(y^{0.5}-x^{0.5})(x^{0.25}*y^{0.5})}{x^{0.5}*y^{0.5}*6})\ frac{4x^{0.25}*x^{0.25}*y^{0.5}}{x^{0.5}*y^{0.5}*6}=\ frac{4x^{0.5}*y^{0.5}}{x^{0.5}*y^{0.5}*6}=frac{2}{3}$