Question

будь ласка спрости вираз (m - n)/(m ^ (1/3) - n ^ (1/3)) - (m + n)/(m ^ (1/3) + n ^ (1/3))

Answer 1

$\displaystyle\bf\\\frac{m-n}{m^{\frac{1}{3} } -n^{\frac{1}{3} } } -\frac{m+n}{m^{\frac{1}{3} } +n^{\frac{1}{3} } } =\frac{(m^{\frac{1}{3} } )^{3} -(n^{\frac{1}{3} } )^{3}}{m^{\frac{1}{3} } -n^{\frac{1}{3} } } -\frac{(m^{\frac{1}{3} } )^{3}+(n^{\frac{1}{3} } )^{3}}{m^{\frac{1}{3} } +n^{\frac{1}{3} } } =$

$\displaystyle\bf\\=\frac{(m^{\frac{1}{3} } -n^{\frac{1}{3} } )(m^{\frac{2}{3} } +m^{\frac{1}{3} } n^{\frac{1}{3} }+n^{\frac{2}{3} } ) }{m^{\frac{1}{3} } -n^{\frac{1}{3} } } -\frac{(m^{\frac{1}{3} } +n^{\frac{1}{3} } )(m^{\frac{2}{3} } -m^{\frac{1}{3} } n^{\frac{1}{3} }+n^{\frac{2}{3} } )}{m^{\frac{1}{3} } +n^{\frac{1}{3} } } =$

$\displaystyle\bf\\=m^{\frac{2}{3} } +m^{\frac{1}{3} } n^{\frac{1}{3} }+n^{\frac{2}{3} } -m^{\frac{2}{3} } +m^{\frac{1}{3} } n^{\frac{1}{3} }-n^{\frac{2}{3} } =2m^{\frac{1}{3} } n^{\frac{1}{3} }$