interval notation for radical 9x/x^2-100?

Question

what is the interval notation of

fraction 9x/x^2-100 inside of a radical

Answer 1

9x/(x^2-100) >= 0

Something happens at x = 0, -10, and 10

Test:  x = -100, -5, 5, 100

x = -100 makes it -

x = -5 makes it +

x = 5 makes it -

x = 100 makes it +

We can't hit x = -10 because that would make the bottom of the equation 0, so at -10 there's a (

We can hit x = 0, so there's a ] at 0

We can't hit x = 10 because that would make the bottom of the equation 0, so at 10 there's a (

(-10,0], (10,Infinity)