Simplify the fraction (3+ 1/x)/(9-1/x^2)

We'll multiply both numerator and denominator by the
largest denominator, namely x^2:
(3x^2 + x^2/x)/(9x^2 - x^2/x^2) = (3x^2 +
x)/(9x^2 - 1)
The difference of two squares from denominator returns the
product:
(9x^2 - 1) = (3x-1)(3x+1)
We'll factorize the numerator by
x:
(3x^2 + x)/(9x^2 - 1) = x(3x+1)/(3x-1)(3x+1)
We'll divide the
fraction by (3x+1):
x(3x+1)/(3x-1)(3x+1) =
x/(3x-1)
Therefore, simplifying the given fraction, we'll get:
x/(3x-1).