Question

X^2 +xy/ x^2 +y^2 * (x/x-y - y/x+y )

Answer 1

Ответ:

Ответ прикрепила

Объяснение:

Answer 2

To simplify the given expression, follow these steps:

1. Factor the numerator and denominator in the fraction.
2. Simplify the fraction as much as possible.

The expression is:

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

Let's start by factoring:

Numerator: x^2 + xy = x(x + y)

Denominator: x^2 + y^2 does not have a simple factorization, so we'll leave it as is.

Now, rewrite the expression:

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

Now, let's simplify the fraction:

1. Cancel out common factors in the numerators and denominators:

(x(x + y)) / (x^2 + y^2) * (x / (x - y) - y / (x + y)) = (x(x + y)) / (x^2 + y^2) * [(x(x + y)) / ((x - y)(x + y)) - (y(x - y)) / ((x - y)(x + y))]

2. Combine the fractions inside the square brackets:

[(x(x + y) - y(x - y)) / ((x - y)(x + y))]

3. Expand the terms in the square brackets:

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

4. Cancel out the xy terms:

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

So, the simplified expression is:

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