SOLUTION: Show by counterexample that (x+y)^-2 and x^-2+y^-2 are not equivalent. please help

You can put this solution on YOUR website!
Proof by Counterexample:


Simply pick two random values for "x" and "y" and plug them in. I'm going to use and (these values are small and nonzero)


Start with the first expression.


Plug in and


Add


Flip the fraction (to make the exponent positive)


Square to get .


So when and


----------------------------------------------------------


Move onto the second expression


Plug in and (note: these values cannot change now)


Flip the fractions (to make the exponents positive)


Square 1 to get 1


Reduce


Add


So when and


----------------------------------------------


Since and when and , this means that