## anonymous 4 years ago I need help please.... Find the domain of the rational function F(x)=-2(x^2-4)/3(x^2+4x+4) I have factored them correctly but it said after I factored them I shouldn't reduce any common factors and should find the domain of the function using its factored form and that I need to state the domain in interval notation. I am lost and do not know how to work this out apparently

$x^2+4x+4\neq0$ $(x+2)^2\neq0$ so the domain interval is:

$x^2+4x+4\neq0$ $(x+2)^2\neq0$ so the domain interval is: $x \in(-\infty,-2)\cup(-2,+\infty)$

3. anonymous

R-{-2}

4. anonymous

Check your nos nena..

to check what?

6. anonymous

I am not understanding...i was told to find the domain of the function using the factored form F(x)=[-2(x-2)(x+2)]/[3(x+2)(x+2)]....how do I work this out

7. anonymous

8. anonymous

Once factored you must use fact the Denominator cannot be zero for any real no

it's ok...:D kcbrosell what part you don't understand?

10. anonymous

all of it I am failing this class big time...I dont understand all the factoring or how to put it into and equation and so on

every time you want to find the domain of the function which is given in fraction form denominator must not be equal to zero, so when you factor x^2+4x+4 you get the result I wrote.....

12. anonymous

I am not understanding how you get to the result u wrote

well it's a basic binomial formula which you must know if you want to do some serious math in the future....

14. anonymous

I got to this point x^2-4=(x-2)(x+2) & x^2+4x+4=(x^2+2)

you got wrong x^2+2x+4...it is (x+2)^2

16. anonymous

o crud...so after I get that worked out do I have to put them into another equation

17. anonymous

|dw:1328644954475:dw|

18. anonymous

if terms like (x+2) cancel, there would normally be a "hole" in the graph...but note that there is still a (x+2) in the denominator, so you must set it equal to zero and solve....this is the value that won't work....so the domain is all of the other numbers....the numbers less than -2 and the numbers greater than -2.

19. anonymous

so then my answer would be (-oo, -2) (-2, oo)

20. anonymous

yes.

21. anonymous

so it all has to do with your neg and pos and how they factor out

22. anonymous

think about what would make the denominator equal to zero...you are correct you often times must factor first to be able to tell.

23. anonymous

okay i thinki understand it a little bit better now thank you for your help

24. anonymous

:)