Simplify the rational expression. State any restrictions on the variable.

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Simplify the rational expression. State any restrictions on the variable.

Mathematics
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@Nnesha do you know anything about this?

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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
opps for some reason I thought i read multiply lol thats what I get for 15 hours of school work today
-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 that means n^4 - 10n^2 + 24 factors to (n^2 - 6)(n^2 - 4) we can then further factor n^2 - 4 down into (n-2)(n+2)
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
Okay so the bottom line reads n^4-9n^2+18 Im confused:/ Would I need to find a number that multiplies to 24 and adds to -9?
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)
n^4 - 10n^2 + 24 completely factors to (n^2 - 6)(n-2)(n+2) n^4-9n^2+18 completely 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
the denominator factors into (n^2-6)(n^2-3) each piece is set equal to 0 and solved for to get n^2-6 = 0 n^2 = 6 n = sqrt(6) or n = -sqrt(6) n^2-3 = 0 n^2 = 3 n = sqrt(3) or n = -sqrt(3)
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
thank you so much!! You are a lifesaver and such a great teacher! My husband usually helps me with math but he doesn't know this type of stuff! Im giving you a medal for your help.
I'm glad it's making more sense now

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