For $Y=X+Z$, I know that $f(X/Y)$ has a Gaussian distribution with mean $\displaystyle\frac{y\sigma^2_x}{\sigma^2_x+\sigma^2_z}$, and variance $\displaystyle\frac{\sigma^2_x\sigma^2_z}{\sigma^2_x+\sigma^2_z}$ if both $X$ and $Z$ are gaussian distribution with means $\mu_x, \mu_z$, and variances $\sigma_x^2, \sigma_z^2$.
I need to know $f(X/Y)$ if $X$ is bimodal Gaussian distribution.