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.
To check if you have reduced the expression to its simplest terms, we can simplify it further. Let's go through the steps to simplify the given expression.
1. Start with the given expression: {(-x - y) * (x - y)} / {(x - y)^2 + (x + y)^2}
2. Simplify the numerator: (-x - y) * (x - y) can be expanded using the distributive property as -x(x) - x(-y) - y(x) - y(-y). This simplifies to -x^2 + xy - xy + y^2, which further simplifies to -x^2 + y^2.
3. Simplify the denominator: (x - y)^2 + (x + y)^2 can be expanded as (x^2 - 2xy + y^2) + (x^2 + 2xy + y^2). Combining like terms, this yields the simplified form: 2x^2 + 2y^2.
4. Substitute the simplified numerator and denominator back into the expression: (-x^2 + y^2) / (2x^2 + 2y^2).
At this point, the expression cannot be simplified any further. Therefore, the simplified form is (-x^2 + y^2) / (2x^2 + 2y^2).