Question

((х-у/х)-(у-х/у))/(х+у/ху)

Answer 1

Ответ:

В решении.

Объяснение:

((х - у)/х - (у - х)/у) : ((х + у)/ху) = х - у.

1) (х - у)/х - (у - х)/у =

общий знаменатель ху:

=[y*(x - y) - x*(y - x)]/xy =

=(ху - у² - ху + х²)/ху =

=(х² - у²)/ху;

2) (х² - у²)/ху : (х + у)/ху =

=(х - у)(х + у)/ху : (х + у)/ху=

= [(х - у)(х + у) * xy] / [xy * (x + y)]=

сократить (разделить) (x + y) и (x + y) на (x + y), ху и ху на ху:

= (х - у) *1/1 * 1 = х - у.

Answer 2

To simplify the expression ((x - y/x) - (y - x/y)) / (x + y/(xy)), you can follow these steps:

1. Find a common denominator for the fractions in the numerator: ((x - y/x) - (y - x/y)) = ((x^2 - y^2) / (x * y)).

2. Now, rewrite the expression with the common denominator: ((x^2 - y^2) / (x * y)) / (x + y/(x * y)).

3. Invert and multiply the denominator of the division by its reciprocal: ((x^2 - y^2) / (x * y)) * ((xy) / (x + y)).

4. Now, multiply the numerators and the denominators together: (x^2 - y^2) * (xy) / (x * y * (x + y)).

5. You can further simplify the expression by factoring the numerator: (x + y)(x - y) * (xy) / (x * y * (x + y)).

6. Notice that (x + y) cancels out in the numerator and the denominator: (x - y) * (xy) / (x * y).

7. Now, you can cancel out the common factors: (x - y).

So, the simplified expression is (x - y).