## anonymous 5 years ago the algebraic expressions x-2 divided by x² -9is undefined when x is ..?

1. anonymous

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

2. anonymous

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

3. 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.

4. anonymous

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

5. anonymous

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

6. anonymous

Is that clearer?

7. anonymous

not really

8. anonymous

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

9. anonymous

yea.. i dont understand that..

10. 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.

11. anonymous

ok

12. anonymous

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

13. anonymous

yes

14. anonymous

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

15. anonymous

2

16. anonymous

Right. Now,

17. anonymous

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

18. anonymous

we could write

19. anonymous

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

20. anonymous

What number would you put in now?

21. anonymous

thats impossible

22. anonymous

EXACTLY

23. anonymous

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

24. anonymous

That's why division by zero is undefined.

25. anonymous

Is that better?

26. anonymous

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

27. anonymous

yeahh

28. 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.

29. 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

30. anonymous

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

31. anonymous

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

32. anonymous

oooooooooooooh alrighttt tanks

33. anonymous

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

34. anonymous

I think it's clicked now :)

35. anonymous

Feel free to become a fan :P

36. anonymous

:D

37. anonymous

lol

38. anonymous

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

39. anonymous

okeydokey