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lian · Feb 28, 2007, 07:06 PM

f(x)= x+2/x+6

Capuchin · Mar 2, 2007, 01:40 AM

Although what az130 says is right, he has missed the negative values that f(x) is positive for too, these are the values below -6.

I have plotted a graph, the blue line is your function, you ca see it is positive above -2 and below -6

at x=-6 I have drawn the asymptote, this is a line that the equation approached but never touches.

Hope this helps.

asterisk_man · Mar 2, 2007, 07:50 AM

Capuchin, can we come up with how to solve this without a graph?

I can do it like this but I'm not happy with it. The second portion seems mathematically correct but obviously leads to the wrong answer. The 0 is causing problems. How do we use algebra to get both answers? How would you find the roots if it were = instead of >? Oh well, it's early for me so maybe my brain will come up to speed later :)

$ \frac {x+2} {x+6} > 0 \\ x+2 > 0 * \left(x+6\right) \\ x > -2 $

and

$ \frac {x+2} {x+6} > 0 \\ \frac {\left(x+6\right)^2} {\left(x+2\right)^2} \frac {x+2} {x+6} > 0 \\ \frac {x+6} {x+2} > 0 \\ x+6 > 0 * \left(x+2\right) \\ x > -6 $

edit: i think the key is that we can't normally multiply both sides by something with an x without causing troubles and like i said, the 0 isn't helping.

Capuchin · Mar 2, 2007, 07:52 AM

Oh yes, I did it in my head without a graph, I just find it easier to show it that way.

Thank you for putting it more clearly than az130

:)