Simplify (1/x + 1/y) / (x/y - y/x)?

....1..........1

------- + -------

....x..........y..........xy

---------------------- x ----------

...x.........y............xy

------- - -------

...y.........x

...y + x

=--------------

...x^2 - y^2

......x + y

=------------------

...(x + y)(x - y)

.......1

=------------ answer//

....x - y

=

1/(x-y)

for this issue you are able to desire to get a user-friendly denominator so for (x/y - y/x) situations each and every by ability of xy and you get (x^2 - y^2 / xy ) for (a million/y + a million/x) you do a similar ingredient and get (x+y /xy) so now you have (x^2 - y^2 / xy) / (x+y/xy) once you divide you are able to turn the (x + y/xy) and multiply so it particularly is : (x^2 - y^2)(xy) / (xy)(x+y) the xy cancels out so which you have x^2-y^2 / x+y x^2-y^2 factors out to be (x-y)(x+y) / (x+y) x+y cancels out and you have answer: x-y

y + x

---------

xy

----------

x ² - y ²

----------

xy

x + y

-----------

x ² - y ²

1

---------

x - y