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Posted by **amy** on Thursday, December 8, 2011 at 5:25pm.

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

- pre cal -
**Reiny**, Thursday, December 8, 2011 at 5:57pmcritical 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

- pre cal -
**amy**, Thursday, December 8, 2011 at 6:17pmThanks I can do it that way but she counts it wrong. That is the answer I got. She wants it in interval notation.

- pre cal -
**Reiny**, Thursday, December 8, 2011 at 6:30pmOh 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".

- pre cal -
**amy**, Sunday, December 11, 2011 at 2:03pmexactly it is what I thought but it does not match her answer sheet so she counts it wrong.

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