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

personally, I do not find it simpler.

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

You are working with the sum of two squares that you cannot factor and the difference of 2 squares that can be factored. Perhaps your teacher just wants you to show that one factorization.

To simplify the expression (x^2 - y^2)/(x^2 + y^2), you can use a common algebraic technique called "difference of squares."

The numerator of the expression, x^2 - y^2, is a difference of squares because it can be factored as (x + y)(x - y). The denominator, x^2 + y^2, cannot be factored further.

So, the simplified expression becomes (x + y)(x - y)/(x^2 + y^2).