I will assume that the denominator is (x+7)(x-5)
or
x^2(9+x)(x-9)/((x+7)(x-5)) ≥ 0
(that is not what you typed)
the critical values are -9, -7, 0, 5, and 9
so pick a value for each domain and evaluate.
We do not need the actual value, just the sign.
1. x< -9 ,
x = -10 ---> +(-)(-)/((-)(-)) = + , so x ≤ 9
2. between -9 and -7
x = -8 ---> +(+)(-)/((-)(-) = - , no good
3. between -7 and 0
x = -5 ---> +(+)(-)/((+)(-) = + , OK
4. the zero ---------- OK
5. between 0 and 5
x = 4 ----> +(+)(-)/((+)(-)) = + , OK
6. between 5 and 9
x = 6 ----> +(+)(-)/((+)(+)) = - , no good
7 x ≥9
x = 10 ----> +(+)(+)/((+)(+)) = + , ok
so x ≤ 9 OR -7 < x < 5 OR x ≥ 9
check out Wolfram
http://www.wolframalpha.com/input/?i=solve+x%5E2%289%2Bx%29%28x-9%29%2F%28%28x%2B7%29%28x-5%29%29+≥+0+
same answer!!
Solve the inequality x^2(9+x)(x-9)/(x+7)(x-5) is greater than or equal to 0?
1 answer