Simplify the expression 9x2 - 1 / 2x + 1

The numerator is $9x^2 - 1$. This can be written as $(3x)^2 - (1)^2$.
Using the difference of squares formula, $a^2 - b^2 = (a-b)(a+b)$, where $a=3x$ and $b=1$:

The original expression is $\frac{9x^2 - 1}{2x+1}$.
Substituting the factored numerator:

The factors in the numerator are $(3x-1)$ and $(3x+1)$. The denominator is $(2x+1)$.
There are no common factors between the numerator and the denominator. Therefore, the expression cannot be simplified further by cancellation.