If $$f(x) = \frac{2x-8}{x^2 -2x - 3} \qquad\text{ and }\qquad g(x) = \frac{3x+9}{2x-4}$$ find the sum of the values of $x$ where the vertical asymptotes of $f(g(x))$ are located.
After expanding , I got : $ 4 ( x^2 - 7x + 10 )/(3x^2 - 20x - 21 )$ , but I am not so sure how to go forward.
Vertical asymptotes are located in points where your function will tend to $\infty$ (denominator tends to $0$, and then depends on the numerator, I let you do the work, you just have to find the points where the polynomials are null)