SOLUTION: I am trying to find the answer to this, and I'm having a lot of problems. ((3x+1)/(9x^2-1)) - ((2)/3x-1))

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I am trying to find the answer to this, and I'm having a lot of problems. ((3x+1)/(9x^2-1)) - ((2)/3x-1))      Log On


   

Question 375997: I am trying to find the answer to this, and I'm having a lot of problems.
((3x+1)/(9x^2-1)) - ((2)/3x-1))
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
((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)