Question

Выполните действия 2m/m^2-4-2/m^2-4:(m+1/2m-2-1/m-1)

Answer 1

$displaystyle frac{2m}{m^2-4}- frac{2}{m^2-4} :bigg( frac{m+1}{2m-2} - frac{1}{m-1} bigg)=\ \ \ = frac{2m}{m^2-4} - frac{2}{m^2-4} : bigg( frac{m+1}{2(m-1)} - frac{2}{2(m-1)} bigg)=\ \ \ = frac{2m}{m^2-4} - frac{2}{m^2-4} : frac{m-1}{2(m-1)} = frac{2m}{m^2-4}- frac{2}{m^2-4}: frac{1}{2} =\ \ \ = frac{2m}{m^2-4} - frac{4}{m^2-4} = frac{2(m-2)}{(m+2)(m-2)} = boxed{frac{2}{m+2} }$