Question 379680
If you started with:

1/9 + 1/3x
------------
x/9 - 1/x

.
to rid ourselves of the denominator, multiply by 9x/9x to get:
.
x + 3
------------
x^2 - 9
.
Next, because the denominator is a "difference of squares" we can factor:
.
x + 3
------------
(x+3)(x-3)
.
Canceling like-terms we finally get:
 1
----
x-3