Question

Найдите значение выражения: (2m+1/2m-1 - 2m-1/2m+1): 4m/10m-5 при m=3/14

Answer 1

1) ( 2m + 1 )/( 2m - 1 ) - ( 2m - 1 )/( 2m + 1 ) = [ ( 2m + 1 )^2 - ( 2m - 1 )^2 ] / ( 4m^2 - 1 )
2) ( 2m + 1 )^2 - ( 2m - 1 )^2 = ( 2m + 1 + 2m - 1 )( 2m + 1 - 2m + 1 ) = 4m•2 = 8m
3) 10m - 5 = 5( 2m - 1 )
4) 8m/ ( ( 2m - 1 )( 2m + 1 )) : 4m/ ( 5( 2m - 1 )) = 10 / ( 2m + 1 )
5) m = 3/14
10 / ( 2•3/14 + 1 ) = 10 / ( 3/7 + 1 ) = 10 / ( 10/7 ) = 7
Ответ 7