Question

(2m+1/2m-1-2m-1/2m+1):4m/10m-5 решите

Answer 1

Ответ:

$\frac{10}{2m+1}$

Объяснение:

$(\frac{2m+1}{2m-1} -\frac{2m-1}{2m+1} ) :\frac{4m}{10m-5} =\frac{10}{2m+1} \\\\1) \frac{2m+1}{2m-1} -\frac{2m-1}{2m+1} = \frac{(2m+1)^{2}-(2m-1)^{2} }{(2m-1)(2m+1)} =\frac{4m^{2} +4m+1-4m^{2}+4m-1 }{(2m-1)(2m+1) } =\frac{8m}{(2m-1)(2m+1) } ;\\\\2) \frac{8m}{(2m-1)(2m+1) } : \frac{4m}{10m-5} = \frac{8m}{(2m-1)(2m+1) } *\frac{5(2m-1)}{4m} = \frac{8m*5(2m-1)}{(2m-1)(2m+1)*4m} =\\\\\frac{10}{2m+1} .$