Does the following expression have a closed form?

Question

I have a ratio that has upper incomplete Gamma functions.

$$ r = \frac{\Gamma(n, (a+c) x) - \Gamma(n, (a+c) y)}{\Gamma(n, a x) - \Gamma(n, a y)} $$

Here, $a, c, x, y$, are positive real and $y > x$. Can this be reduced further to a nice form?