Question

Which graph shows the solution set of x^2+9+20/x^2-x-20 > 0

Answer 1

Before we do anything, we can factorize the numerator and denominator:

`(x^2+9x+20)/(x^2-x-20)=((x+5)(x+4))/((x-5)(x+4))=(x+5)/(x-5)`

(the cancellation is valid as long as
`x\\eq-4`;
`x=-4` is not even in the domain of the right hand side, so we're good here)

Then

`\drac{x+5}{x-5}=(x-5+10)/(x-5)=1-(10)/(x-5)>0\implies1>(10)/(x-5)`

`\implies10<x-5\implies x>15`

Answer 2

option B

Explanation:

edg 2022