Question

Find all numbers for which the rational expression is undefined.

(n^3-3n)/(n^2-9)

Answer 1

alright what do you know about when your equation is undefined?

Answer 2

ummm...nothing?

Answer 3

alright so we'll start with the basis idea that is used all the way through to calculus.

is \[\frac{1}{0},\frac{25}{0},\frac{x}{0}\] computable?

Answer 4

how do i tell?

Answer 5

no, because nothing is divisible by 0

Answer 6

well for one, when you put this into a calculator, what does it tell you?

Answer 7

it says cannot divide by zero

Answer 8

correct it's undefined =nothing.. so in your case you have a the same type of fraction only with variables

Answer 9

so you don't have to worry about the numerator, just the denominator; you want the denominator to equal zero because in this case the problem will be undefined

Answer 10

okay, n^2-9=0?

Answer 11

yep do you know how to solve this equation

Answer 12

nope

Answer 13

well you can either tell that it's a difference of two squares which has the equation

\[(a^2-b^2)=(a+b)(a-b)\]

or you can simply solve it by using algebra and

adding the 9 over to right side to get

\[x^2=9\]

in which you take the square root of both sides

Answer 14

so, x=3?

Answer 15

if you did the square root way you get a positive and negative answer

\[x=+3,-3\]

if you did the difference method you find out that b = 3 and a = x


so theequation is

(x+3)(x-3)=0

which you get

x+3=0
and
x-3=0

x=-3,+3

Answer 16

since x^2 turns any integer positive, it can be negative or positive

(-3)^2=9-9=0

(3)^2=9-9=0

Answer 17

I don't understand the relation between my fraction and that formula...

Answer 18

the difference formula you mean?

Answer 19

thoroughly confused

Answer 20

I'm working on y alg 2 final...and I am so lost, confused and frustrated...

Answer 21

alright you have

\[n^2-9=0\]

these are two perfect square. by perfect squares i mean that if you take the square root of each you get an integer

so if you use

\[a^2+b^2=(a+b)(a-b)\]

where

\[a^2=n^2,b^2=9\]

you know that

taking the square root you get

a=n
b=3

so then you just use the rest of the formula

Answer 22

(n-3)(n+3)=0

now the way to make this equation zero is making one of the groups turn to zero because if you do that the whole equation will become zero... so say you make n+3=0, n would have to equal -3 right?

(-3-3)(-3+3)=0

(-6)(0)=0
0=0

Answer 23

does wher you put the plus or minus matter?

Answer 24

for the answers? or for the equation

the equation can be (a+b)(a-b) or (a-b)(a+b) if that's what you're asking.

Answer 25

that's what I was asking

Answer 26

yeah it'st he same as multiplying say (3) and (4)

3(4)=12
4(3)=12

Answer 27

oh, okay

Answer 28

Thank you

Answer 29

No problem =]