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what two numbers multiply to 24 and add to -10?

12 and 2

nope

12+2 = 14 not -10

|dw:1444458852967:dw| I believe this is the answer

-6 and -4 fit the description, no?
-6 + (-4) = -10
-6 times -4 = 24

Yes that is correct. I see what you mean by that now

so overall, n^4 - 10n^2 + 24 completely factors to (n^2 - 6)(n-2)(n+2)

you'll do the same for the denominator and see if you can cancel anything

multiplies to 18 actually

find two numbers that multiply to 18 and add to -9

so 6 and 3 right cause 6*3=18 and -6+-3=-9

-6 and -3

I think that's what you meant to say?

right

so n^4-9n^2+18 factors to (n^2-6)(n^2-3)

at this point, I see a pair of terms cancelling

n^2-6

yes

so (n^2-2) (n+2)
(n^2-3)
(n^2-4)
(n^2-3)

I think you meant to say `(n-2) (n+2)` in your first step

but yeah the final answer is \[\Large \frac{n^2-4}{n^2-3}\]

what would the restrictions be?

so would the answer be this |dw:1444460035990:dw|

close

but no

could we work the problem out further? I quess i still dont 100% understand

would it be the square root of those numbers ( 6, -3)

so the restrictions are actually
\[\Large n \ne \pm \sqrt{6}\]
\[\Large n \ne \pm \sqrt{3}\]

|dw:1444460209535:dw|

much better

I'm glad it's making more sense now