Question

1÷x-y - 1÷y-x - 2x÷x²-y²

Answer 1

Ответ:1÷х-у-1÷у-х-2х÷х2÷у2

1/х-у-1/у-х-2х/х2-у2

Объяснение:

Answer 2

To simplify the expression, let's first find common denominators for each term and then combine them.

1. Finding common denominators: For the first term, 1/(x - y), the common denominator is (x - y). For the second term, 1/(y - x), the common denominator is -(x - y) (notice the negative sign). For the third term, 2x/(x^2 - y^2), the common denominator is (x + y)(x - y) (difference of squares).

2. Writing the terms with their common denominators: 1/(x - y) - 1/(y - x) - 2x/(x^2 - y^2)

3. Simplifying each term:

a) 1/(x - y) - 1/(y - x): Since (y - x) = -(x - y), the expression becomes: 1/(x - y) - 1/-(x - y) => 1/(x - y) + 1/(x - y)

Now, combine the terms with the common denominator: (1 + 1)/(x - y) = 2/(x - y)

b) 2x/(x^2 - y^2): This can be simplified as follows: 2x/(x^2 - y^2) = 2x/[(x + y)(x - y)]

4. Final expression: Now, combining the simplified terms from step 3, we get the final expression: 2/(x - y) - 2x/[(x + y)(x - y)]

To further simplify, we can take out the common denominator, which is (x - y), from both terms: 2/(x - y) - 2x/[(x + y)(x - y)] = (2(x + y) - 2x)/[(x + y)(x - y)]

Now, simplify the numerator: 2(x + y) - 2x = 2x + 2y - 2x = 2y

The expression becomes: 2y/[(x + y)(x - y)]

So, the simplified expression is 2y/[(x + y)(x - y)].