Question

(x^2-x-20)/(x^2-4x-12) >0

I'm not really sure how to solve this inequality. I can understand to simplify the top and bottom which turns it into

((x-5)(x+4))/((x-6)(x+2))

but I don't know what to do next

Answer 1

you know there are asymptotes or zeroes at x = -4, -2, 5 and 6
At each of those points, y changes sign, because exactly one of the factors changes sign. So, for x < =4, all the factors are negative, so y is positive.
So, y is
positive on (-∞,-4)
negative on (-4,-2)
positive on (-2,5)
negative on (5,6)
positive on (6,∞)

See the graph at

https://www.wolframalpha.com/input/?i=%28x%5E2-x-20%29%2F%28x%5E2-4x-12%29