  In this paper, using inverse integral transforms, we derive the exact
distribution of the random variable $X$ that is involved in the ratio $Z
\stackrel{d}{=} X/(X+Y)$ where $X$ and $Y$ are independent random variables
having the same support, and $Z$ and $Y$ have known distributions. We introduce
new distributions this way. As applications of the obtained results, several
examples are presented.
