Write the form of the partial fraction decomposition of the rational expression.
1/9x^2-4
To find the partial fraction decomposition of a rational expression, you first need to factor the denominator completely.
The denominator in this case is 9x^2 - 4. It's a difference of squares, so we can factor it as (3x)^2 - 2^2.
Next, we can use the difference of squares formula, which states that a^2 - b^2 = (a + b)(a - b).
Therefore, we get (3x)^2 - 2^2 = (3x + 2)(3x - 2).
Now that we have factored the denominator completely, we can write the partial fraction decomposition:
1/(9x^2 - 4) = A/(3x + 2) + B/(3x - 2)
Here, A and B are constants that we need to find.