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

- anonymous

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

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- anonymous

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

- anonymous

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

- anonymous

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.

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## More answers

- anonymous

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

- anonymous

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

- anonymous

Is that clearer?

- anonymous

not really

- anonymous

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

- anonymous

yea.. i dont understand that..

- anonymous

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.

- anonymous

ok

- anonymous

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

- anonymous

yes

- anonymous

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

- anonymous

2

- anonymous

Right. Now,

- anonymous

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

- anonymous

we could write

- anonymous

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

- anonymous

What number would you put in now?

- anonymous

thats impossible

- anonymous

EXACTLY

- anonymous

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

- anonymous

That's why division by zero is undefined.

- anonymous

Is that better?

- anonymous

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

- anonymous

yeahh

- anonymous

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.

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

oooooooooooooh alrighttt tanks

- anonymous

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

- anonymous

I think it's clicked now :)

- anonymous

Feel free to become a fan :P

- anonymous

:D

- anonymous

lol

- anonymous

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

- anonymous

okeydokey

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