Finding percentage when infinity is involved

Question

Is it possible to convert a function of the form $f(x)=ax/(a-x)$ to a form where you can find $f(x)/f(a)$? I'd like to find the percentage of $f(a)$ for $f(x)$ but this seems impossible while $f(a)$ is infinite.

Answer 1

$$ \lim_{b\to a} \frac{f(x)}{f(b)} = \lim_{b\to a} \frac{ax/(a-x)}{ab/(a-b)} = \lim_{b\to a} \frac{ax(a-b)}{ab(a-x)} = \frac{ax(a-a)}{a^2(a-x)} = 0. $$

If the denominator approaches $\infty$ while the numerator approaches a finite number, then the whole fraction approaches $0$.

If the numerator and denominator had both approached $\infty$, then the whole fraction might have approached some finite number.