Simplify and identify the domain.

- anonymous

Simplify and identify the domain.

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- anonymous

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- mathslover

You need to first factorize the denominator. Can you do it?

- anonymous

i barley started to learn this, so would you mind leading me through it

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## More answers

- anonymous

i will post the answer choices!

- mathslover

Yeah, sure! No problem!
See :
I've denominator as : \((4x + 8).(x^2 - 9) \)
I'll factorize both of them separately.
\(4x + 8\) can be written as : \(4(x+2)\) ; Notice what I did... I just took 4 common from both the terms and I was left with (x+2).
Clear with this part?

- anonymous

@jagr2713

- anonymous

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- anonymous

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- anonymous

@jagr2713

- anonymous

the last choice should have a parenthesis at the end

- anonymous

are you there? @jagr2713

- anonymous

@peachpi

- anonymous

Let's factor 4x + 8.
What is the biggest number that goes into both 4 and 8?

- anonymous

that divides into both of them? 4

- anonymous

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- anonymous

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- anonymous

im kinda confused?

- anonymous

have you done factoring yet in school?

- anonymous

I'm only asking you to reduce the 2 fractions inside the parentheses right now

- anonymous

do you know how to put 4/4 in lowest terms?

- anonymous

not really!! and not i barley started learning to factor!

- anonymous

the question you posted is relatively advanced algebra. I'm not really sure how to help you if you aren't even familiar with the basic stuff. :(

- anonymous

well it is a worksheet that we are suppose to get help with to start becoming familiar with this topic!

- anonymous

@peachpi can you just try to walk through it with me? please!!

- anonymous

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- anonymous

does that make sense?

- anonymous

oh okay so the cancel out!

- anonymous

yes. now to factor xÂ² - 9. There is no common factor, so we have to use another rule. What number times itself is 9?

- anonymous

in other words, what's the square root of 9?

- anonymous

3

- anonymous

this rule is called a difference of squares.
xÂ² - 9 = (x - 3)(x + 3)

- anonymous

okay!

- anonymous

so then it whould equal to zero?

- anonymous

so 3 and -3?

- anonymous

yes.
but you also have to do 4x+8 = 0

- anonymous

ok

- anonymous

how do i do that one?

- anonymous

start by subtracting 8 from both sides

- anonymous

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- anonymous

4x=-8

- anonymous

how do you get x by itself from there?

- anonymous

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- anonymous

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- anonymous

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- anonymous

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- anonymous

so your answers for the exclusions
\[x \neq -3, -2, 3\]

- anonymous

okay!

- anonymous

now let's get back to the simplifying part. I'm going to rewrite the expression to show the factoring

- anonymous

so as of now the possible answers are b and d! correct?

- anonymous

yes

- anonymous

okay!

- anonymous

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- anonymous

|dw:1433130238835:dw| is this right?

- anonymous

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- anonymous

@peachpi

- anonymous

is my simplifying correct?

- anonymous

that's right :)

- anonymous

so b?

- anonymous

yes

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