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

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];