(x-y)/(x+y)(x-y) is it legal to remove (x-y) leaving me with 1/(x+y) ?

Question

(x-y)/(x+y)(x-y) is  it legal to remove (x-y) leaving me with 1/(x+y) ?

anonymous · Answer

yes it is :)

anonymous · Answer

you can cancel (x-y) from top and bottom ^_^

anonymous · Answer

As long as $$x \neq y$$.

anonymous · Answer

now why would x = y?

anonymous · Answer

you can just simply simplify without looking at that condition ^_^

anonymous · Answer

ok thanks!

anonymous · Answer

np :)

amistre64 · Answer

(x-y)
--------
(x+y)(x-y)

What looks like "canceling" like terms top to bottom is actually misleading.

What you are doing is seperating the fraction into parts; and anything that is equal to (1) stays there, but is implied.

  1       (x-y)           1
----   ----   =  ----  times  (1) 
(x+y)   (x-y)        (x+y)

anonymous · Answer

You must have the condition that x does not equal y. Because along the line x=y you will have a discontinuity in your graph. Specifically a hole I think. The function is not defined there.

amistre64 · Answer

If we are talking about the graph of the function, then you are correct.  If we can "cross out" like terms it will create a hole in the graph, a jump discontinuity.