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

Question 185459: Show by counterexample that (x+y)^-2 and x^-2+y^-2 are not equivalent. please help
Answer by jim_thompson5910(35256) (Show Source): 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

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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

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Since and when and , this means that
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