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

Engr. Ronald2011-09-16T05:50:05Z

Favorite Answer

....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

=

Ling Ling2011-09-16T05:35:26Z

1/(x-y)

?2016-12-01T07:43:27Z

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

Como2011-09-16T09:08:37Z

y + x
---------
xy
----------
x ² - y ²
----------
xy

x + y
-----------
x ² - y ²

1
---------
x - y