It is possible to find the CDF?

It is possible to find the CDF?

I have a problem as follows:
$X_i$ and $Y_j$ , $i=1\ldots N$ and $j=1\ldots K$ are random variables
distributed as following CDF: \begin{align} F_{X_i}(x)=1-\frac{1}{Ax+1}
\exp\left( -\frac{x}{B} \right) \\ F_{Y_i} (y)=1-\frac{1}{Cy+1} \exp\left(
-\frac{y}{D} \right) \end{align}
Let define $Z=\frac{1+ \max \{ {X_i} \} }{1+ \max\{Y_j\}}$ to be an random
variable.
Find the CDF of Z, i.e., $\Pr\{Z<z\}$.
I dont know how to do it? Could you please help me to find the CDF ?
Thanks for your help!