Question

How do you solve `(16-x^2)/(x^2-9)>=0`?

Answer 1

`3<|x|<=4` alternatively `3<x<=4` or `-4<=x<-3`

Explanation:

For the inequality to be two either `16-x^2>=0 and x^2-9>=0` or `16-x^2<=0 and x^2-9<=0`
Note that `|x|=3` is not defined
Now `16-x^2>=0` if `|x|<=4` and `x^2-9>=0` if `|x|>3` so `3<|x|<=4`
Now `16-x^2<=0` if `|x|>=4` and `x^2-9<=0` if `|x|<3` which has no solution