solve the inequality express your solution in interval notation

Question

(x - 4)^2/ (x -6) (x + 6) > 0 Help me!

Answer 1

critical values of x are
x = 4, -6 and 6

Pick any x in the sections of the number line marked by these values
We don not have to do the actual calculation , just consider what happens to the signs

x < -6, say x=-10
+/-- > 0 good
x between -6 and 4, say x=0
+/- + < 0 NO
x between 4 and 6 , say x=5
+/- + <0 , NO
x > 6, say x=10
+/+ + > 0, good

so x < -6 or x > 6

Wolfram shows the graph and illustrates my solution is correct
http://www.wolframalpha.com/input/?i=%28x+-+4%29%5E2%2F+%28x+-6%29+%28x+%2B+6%29+%3Dy

Answer 2

Thanks I can do it that way but she counts it wrong. That is the answer I got. She wants it in interval notation.

Answer 3

Oh my!
That would be expressing it in a different form, I think it would be something like
(-∞ , -6) or (6,∞)

x < -6 or x > 6 says the same thing in a different way, but it certainly is not "wrong".

Answer 4

exactly it is what I thought but it does not match her answer sheet so she counts it wrong.