Question

Упростите,пожалуйста

Answer 1

$\displaystyle\tt\bigg(\frac{m^{\frac{1}{2}}+1}{m^{\frac{1}{2}}-1}-\frac{m^{\frac{1}{2}}-1}{m^{\frac{1}{2}}+1}\bigg)\cdot\bigg(\frac{m^{\frac{3}{2}}}{2}-\frac{1}{2m^{\frac{1}{2}}}\bigg)=\frac{(m^{\frac{1}{2}}+1)^2-(m^{\frac{1}{2}}-1)^2}{(m^{\frac{1}{2}}-1)(m^{\frac{1}{2}}+1)}\cdot \frac{m^{\frac{3}{2}}\cdot m^{\frac{1}{2}}-1}{2m^{\frac{1}{2}}}=\\\\\\=\frac{(m^{\frac{1}{2}}+1-m^{\frac{1}{2}}+1)(m^{\frac{1}{2}}+1+m^{\frac{1}{2}}-1)}{m-1} \cdot \frac{m^2-1}{2m^{\frac{1}{2}}} =$

$\displaystyle\tt \\\\\\ =\frac{2\cdot2m^{\frac{1}{2}}}{m-1}\cdot\frac{(m-1)(m+1)}{2m^{\frac{1}{2}}} = 2(m+1)=2m+2$