Question

How do I find the numbers that must be excluded from the domain or the rational expression?:

Answer 1

\[\frac{ 9 }{ x-6 }\]

Answer 2

domain are those values for which the expression is defined

Answer 3

here at x=6 the expression becomes undefined
thus 6 must be excluded from domain

Answer 4

How does that work though?

Answer 5

since the denominator will become zero at x-6=0 i.e. at 6

Answer 6

So what would you do for \[\frac{ 4 }{ x+3 }\]

Answer 7

I have a whole section on this and it just gets harder, and I truly don't understand it.

Answer 8

x + 3 = 0
i.e. at -3

Answer 9

God, this makes no sense....how is it -3?

Answer 10

i think u r not getting my point.. oK

Answer 11

Sorry :/

Answer 12

Really? I need helppppppppp!

Answer 13

what is the definition of domain?

Answer 14

values for which the expression is defined

Answer 15

and whats the question?

Answer 16

u need to find those values which are excluded from domain..is it..

Answer 17

Yes

Answer 18

so
make that attempt in such a way that the expression becomes undefined

Answer 19

undefined?

Answer 20

u don;t understand undefined

Answer 21

the opposite of defined

Answer 22

What does that mean, though? what defines a rational expression?

Answer 23

if u get a real number it becomes defined
if u get 1/0 case or 0/0 case it is known as undefined

Answer 24

So what exactly makes the 6 in the 9/x-6 expression excluded from the domain?

Answer 25

yes

Answer 26

thank GOD .. lol

Answer 27

....what?

Answer 28

nothing

Answer 29

have u understood now?

Answer 30

No, otherwise I wouldn't have asked that

Answer 31

what u haven't understood ?

Answer 32

Why the 6 is excluded

Answer 33

because at 6 the expression becomes 9/0 case which is undefined

Answer 34

what makes it defined?

Answer 35

if the number in denominator is 0 in any case it is undefined

Answer 36

otherwise it is defined

Answer 37

so what about with 4/x+3...why is -3 excluded? how did you get -3?

Answer 38

since at -3 denominator will become zero

Answer 39

ohhhhhhh!!!
Alright, I see now! What about with more complex expressions like: \[\frac{ x-3 }{ x ^{2}-64 }\]

Answer 40

u try first

Answer 41

well, do I have to do anything with the x^2?

Answer 42

at what value will make denominator zero?

Answer 43

64?

Answer 44

make denominator equal to zero
x^2-64=0

Answer 45

find x

Answer 46

But how? Like: (x+8)(x-8)?

Answer 47

yeah ... u will get x=8,-8

Answer 48

So, those are the only answers?