Question

Simplify (x^-1-(x+1)^-1)^-2

Answer 1

x^-1 = 1 / x ;
( x + 1 )^-1 = 1 / ( x + 1 ) ;
Then, x^-1 - ( x + 1 )^-1 = 1 / x - 1 / ( x + 1 ) = ( x + 1 ) / [x( x + 1 )] - x / [x( x + 1 )] = ( x + 1 - x ) /[x( x + 1 )] = 1 / [x( x + 1 )];
Finally, (1 / [x( x + 1 )])-2 =[x( x + 1 )]^2 = (x^2)[( x + 1 )^2] ;