homework and exercises - Inverse Quantum Operator

In the quantum harmonic oscillator problem, how would one go about calculating

$$\left\langle n\left|\frac{1}{X^2}\right|n\right\rangle$$

using raising and lowering operators $a^{\dagger}, a$ only, where $X\propto a + a^{\dagger}$ is a linear combination of the raising and lowering operators?

It would also be helpful if someone could refer me to materials on properties of functions of quantum operators.