Use the partial fractions method to express the function as a power series (centered at $x=0$) and then give the open interval of convergence.

$$f(x) = \frac{3 x +4}{4 x^2 - 11 x - 3}$$

$f(x) = \displaystyle \sum\limits_{n=0}^{\infty}$

The open interval of convergence is: (Give your answer in interval notation.)