Question

the algebraic expressions x-2 divided by x² -9is undefined when x is ..?

Answer 1

It's undefined when the denominator is 0. This occurs when \[x^2-9=0 \rightarrow x=\pm 3\]

Answer 2

if the denominator is zero than wouldnt the answer be zero?

Answer 3

No, the denominator is zero for x-values such that \[x^2-9=0\]
By what you're saying, if the answer is zero, x=0. But then the denominator would be \[0^2-9=-9\]which is fine. You can divide your expression by -9.

Answer 4

\[\frac{x-2}{x^2-9}=\frac{something}{0}\]is undefined.

Answer 5

You have to find the x-values that make the denominator 0.

Answer 6

Is that clearer?

Answer 7

not really

Answer 8

Is it the 'undefined' thing, i.e. *why* you have to find x where x^2-9 = 0?

Answer 9

yea.. i dont understand that..

Answer 10

Okay. In division, you can't ever divide by 0. This is because, if we did it, we wouldn't actually end up with something that made sense. I'll give you a simple example.

Answer 11

ok

Answer 12

You're happy with\[\frac{6}{2}=3\] yeah?

Answer 13

yes

Answer 14

So if I then write,\[6=\left[ ? \right]\times 3\]what number would you put in there?

Answer 15

2

Answer 16

Right. Now,

Answer 17

if we imagine \[\frac{6}{0}=\left[ ? \right]\](i.e. *some* number)

Answer 18

we could write

Answer 19

\[6=0 \times \left[ ? \right]\]

Answer 20

What number would you put in now?

Answer 21

thats impossible

Answer 22

EXACTLY

Answer 23

We attempted to divide 6 by 0 and ended up with an IMPOSSIBILITY.

Answer 24

That's why division by zero is undefined.

Answer 25

Is that better?

Answer 26

This will happen no matter what you try to divide by zero.

Answer 27

yeahh

Answer 28

So that's why you have to find all the x-values that will end up making x^2-9 = 0 ... because everything falls apart there.

Answer 29

If x is 3 or -3,

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

Answer 30

\[\frac{x-2}{x^2-9}=\frac{3 -2}{3^2-9}=\frac{1}{0}\]when x=3

Answer 31

\[\frac{x-2}{x^2-9}=\frac{-3-2}{(-3)^2-9}=\frac{-5}{0}\]when x=-3.

Answer 32

oooooooooooooh alrighttt tanks

Answer 33

In both cases, you'll end up with the same rubbish you get with \[\frac{6}{0}\]

Answer 34

I think it's clicked now :)

Answer 35

Feel free to become a fan :P

Answer 36

:D

Answer 37

lol

Answer 38

Good luck with your algebra. Try and link it to numbers if you have trouble.

Answer 39

okeydokey