Question 375997
((3x+1)/(9x^2-1)) - ((2)/3x-1))
.
Notice that
(9x^2-1)
can be written as a "difference of squares":
((3x)^2-1^2)
which can be factored as:
(3x-1)(3x+1)
.
So,we can rewrite:
((3x+1)/(9x^2-1)) - ((2)/3x-1))
as
((3x+1)/((3x-1)(3x+1))) - ((2)/3x-1))
canceling like-terms:
(1/(3x-1)) - ((2)/3x-1))
Now we can combine as:

(1-2)/(3x-1)

-1/(3x-1)
or
1/(1-3x)