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).