Can someone please check this to see if I have reduced to simplest terms:

{(-x-y)X(x-y)}/ {(x-y)^2 + (x+y)^2}

I get -1/2 (x-y)(x+y)divided by (x^2+y^2).
Is this right and if so, can it be simplified any more? Thanks so much.

It is correct, although you could also put it as

-(1/2)(x²-y²)/(x²+y²)
since (x-y)(x+y)=x²-y²

Thanks so much!

You're very welcome!

To check if the expression has been reduced to its simplest terms, you can simplify it further by canceling common factors in the numerator and denominator.

Starting with the expression:

{(-x-y)X(x-y)}/ {(x-y)^2 + (x+y)^2}

Let's first simplify the numerator:

-1 * (x-y) * (x-y) = -(x-y)^2

Now let's simplify the denominator:

(x-y)^2 + (x+y)^2 = x^2 - 2xy + y^2 + x^2 + 2xy + y^2 = 2x^2 + 2y^2

Putting the simplified numerator and denominator together, we get:

-(x-y)^2 / (2x^2 + 2y^2)

This is the simplest form of the expression, and it cannot be simplified any further. Therefore, your answer of -1 * (x-y)(x+y) / (x^2 + y^2) is correct, and it has been reduced to its simplest terms.