Symmetric Function of Quadratic Roots

Let $r$ and $s$ be the roots of the polynomial $x^2 + 2x + 3$. What is the value of $\frac{1}{r^2 - 1} + \frac{1}{s^2 - 1}$? The answer is in the form $-\frac{\alpha}{\beta}$ for coprime integers $\alpha$ and $\beta$. Input the answer as the sum $\alpha +\beta$.