PDF of $\tfrac{aX}{b + cX}$

Question

How to find the PDF of $$Y \triangleq \dfrac{aX}{b + cX},$$ where $a, b, c > 0$. Moreover, $X$ is a random variable with PDF given as $$f_{X}(x) = \dfrac{1}{\Omega} \exp \left( \dfrac{-x}{\Omega}\right); \quad x \geq 0, \Omega > 0$$

I have no idea, how to proceed. I'd be very much thankful if anyone can give any hint to proceed. Thanks!

Edit: Correction in $f_{X}(x)$ after getting the comment.

Answer 1

Hint: $$\Pr\left(Y \le y\right)=\Pr\left(\frac{aX}{b+cX} \le y\right) = \Pr\left(X \le \frac{by}{a-cy}\right).$$