Question

Сократить дробь (m+n)/(m^(1/3)-n^(1/3))

Answer 1

Ответ:

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

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