Question

Помогите пожалуйста!!

Answer 1

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

$= \frac{(m^{\frac{1}{2}}+n^{\frac{1}{2}})^2-(m+m^{\frac{1}{2}}n^{\frac{1}{2}}+n)}{m^{\frac{1}{2}}+n^{\frac{1}{2}}} = \frac{m+2m^{\frac{1}{2}}n^{\frac{1}{2}}+n-m-m^{\frac{1}{2}}n^{\frac{1}{2}}-n}{m^{\frac{1}{2}}+n^{\frac{1}{2}}} =\\\\= \frac{m^{\frac{1}{2}}n^{\frac{1}{2}}}{m^{\frac{1}{2}}+n^\frac{1}{2}} = \frac{\sqrt{mn}}{\sqrt{m}+\sqrt{n}}$