More help on algebra please?

- anonymous

More help on algebra please?

- jamiebookeater

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- anonymous

Rationalize the denominator and simplify \[\frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}+2 }\] Once again I know I need to multiply it by the conjugate but again I need help doing the actual math.
I multiplied it by \[\frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}-2 }\] and I got \[\frac{ 1-\sqrt{a+1} }{ -1 }\] but it doesn't fit where I need to put the answer.

- UsukiDoll

sigh it's nice to know that someone is doing latex.. it sucks that my fraction latex is broken .

- anonymous

latex?

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## More answers

- UsukiDoll

\[\frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}+2 } \cdot \frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}-2 } \]

- UsukiDoll

yeah that's used to type Math. It's called Latex. But on my end it's coo coo

- anonymous

Ohh

- UsukiDoll

\[\frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}+2 } \cdot \frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}-2 } \rightarrow \frac{(\sqrt{a+1}-2)(\sqrt{a+1}-2)}{(\sqrt{a+1}+2)(\sqrt{a+1}-2)}\]

- UsukiDoll

can we not give direct answers please? It's against code of conduct

- LilyMQ

oh sorry I'm new here

- LilyMQ

deleted

- UsukiDoll

ah. I see. Ok.

- anonymous

@LilyMQ I do need to know how

- UsukiDoll

You can read more about the code of conduct here. http://openstudy.com/code-of-conduct

- UsukiDoll

anyway where was I?
\[\frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}+2 } \cdot \frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}-2 } \rightarrow \frac{(\sqrt{a+1}-2)(\sqrt{a+1}-2)}{(\sqrt{a+1}+2)(\sqrt{a+1}-2)}\]

- UsukiDoll

so we need to use the foil method... as usual the denominator is always easier because the middle terms are cut out

- UsukiDoll

\[\frac{(\sqrt{a+1}-2)(\sqrt{a+1}-2)}{(\sqrt{a+1}+2)(\sqrt{a+1}-2)} =\frac{?}{(a+1)-4}\]

- UsukiDoll

so foil is needed on the numerator .

- UsukiDoll

our denominator should be a+1-4=a-3

- UsukiDoll

dear gawd latex... U SUCK!
|dw:1437556072647:dw|

- anonymous

Ok I'm following

- UsukiDoll

so now all we need to do is apply foil method to the numerator
\[\frac{(\sqrt{a+1}-2)(\sqrt{a+1}-2)}{(\sqrt{a+1}+2)(\sqrt{a+1}-2)} =\frac{?}{a-3}\]
so foil is first outer inner last
\[\ \frac{\sqrt{a+1} \sqrt{a+1}-2 \sqrt{a+1}-2 \sqrt{a-1}+(-2)(-2)}{a-3}\]

- UsukiDoll

-_-

- anonymous

It actually looks fine on my side

- Jhannybean

Yeah same here |dw:1437556324233:dw|

- anonymous

Ok so we end up with \[a+1-2\sqrt{a+1}-2\sqrt{a+1}+4\] but I'm not sure?

- Jhannybean

Remember your polynomial expansion : \((a-b)^2 = a^2 -2ab+b^2\)

- Jhannybean

And take \(a= \sqrt{a+1}\) and \(b = -2\)

- UsukiDoll

well a square root times a square root will just be that result so in that case it's just a+1
then (-2)(-2) is 4
you can combine the middle terms

- anonymous

Not sure how to combine the middle terms but I know they are both \[-2\sqrt{a+1}\]

- UsukiDoll

\[a+1-2\sqrt{a+1}-2\sqrt{a+1}+4 \] yes they both have negative signs ... factor out the square root a+1 and then do -2-2

- UsukiDoll

yeah ...we're supposed to have -4\sqrt{a+1}

- UsukiDoll

I would ignore the a+1 in the square root part and just compute -2-2

- Jhannybean

\[-2ab \rightarrow -2(\sqrt{a+1})(2)\] in correctingmy error.

- anonymous

OK so I got the final answer and I figured out my error the first time and as usual it was just a simple math slip. The final answer is \[\frac{ 5+a-4\sqrt{a+1} }{ a-3 }\]

- Jhannybean

That looks correct

- anonymous

Oh my gosh wow it took me a long time but I got 100% XD

- UsukiDoll

\[a+1-2\sqrt{a+1}-2\sqrt{a+1}+4 \rightarrow \frac{a-4\sqrt{a+1}+5}{a-3}\]

- anonymous

Thanks

- UsukiDoll

yup it's correct XD

- anonymous

I'm still way behind on summer school but oh well lol

- UsukiDoll

ouch. how much more material do you have to complete?

- anonymous

I'm three percent done and I need to be 100% by August 1 XD

- anonymous

Plus I need to be 100% done on another class too by that time

- anonymous

So it's gonna be crunch time XD

- UsukiDoll

oh. time for all nighters. Drink tons of coffee!

- anonymous

Yup

- UsukiDoll

Hmm if you complete 20% of the material, you'll get it done in 5 days XD! So that makes it July 26.

- anonymous

Good plan I'll just get 20% done a day and I'll be done just on time XD

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