anonymous
  • anonymous
More help on algebra please?
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • 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
  • UsukiDoll
sigh it's nice to know that someone is doing latex.. it sucks that my fraction latex is broken .
anonymous
  • anonymous
latex?

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More answers

UsukiDoll
  • UsukiDoll
\[\frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}+2 } \cdot \frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}-2 } \]
UsukiDoll
  • UsukiDoll
yeah that's used to type Math. It's called Latex. But on my end it's coo coo
anonymous
  • anonymous
Ohh
UsukiDoll
  • 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
  • UsukiDoll
can we not give direct answers please? It's against code of conduct
LilyMQ
  • LilyMQ
oh sorry I'm new here
LilyMQ
  • LilyMQ
deleted
UsukiDoll
  • UsukiDoll
ah. I see. Ok.
anonymous
  • anonymous
@LilyMQ I do need to know how
UsukiDoll
  • UsukiDoll
You can read more about the code of conduct here. http://openstudy.com/code-of-conduct
UsukiDoll
  • 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
  • UsukiDoll
so we need to use the foil method... as usual the denominator is always easier because the middle terms are cut out
UsukiDoll
  • UsukiDoll
\[\frac{(\sqrt{a+1}-2)(\sqrt{a+1}-2)}{(\sqrt{a+1}+2)(\sqrt{a+1}-2)} =\frac{?}{(a+1)-4}\]
UsukiDoll
  • UsukiDoll
so foil is needed on the numerator .
UsukiDoll
  • UsukiDoll
our denominator should be a+1-4=a-3
UsukiDoll
  • UsukiDoll
dear gawd latex... U SUCK! |dw:1437556072647:dw|
anonymous
  • anonymous
Ok I'm following
UsukiDoll
  • 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
  • UsukiDoll
-_-
anonymous
  • anonymous
It actually looks fine on my side
Jhannybean
  • Jhannybean
Yeah same here |dw:1437556324233:dw|
anonymous
  • anonymous
Ok so we end up with \[a+1-2\sqrt{a+1}-2\sqrt{a+1}+4\] but I'm not sure?
Jhannybean
  • Jhannybean
Remember your polynomial expansion : \((a-b)^2 = a^2 -2ab+b^2\)
Jhannybean
  • Jhannybean
And take \(a= \sqrt{a+1}\) and \(b = -2\)
UsukiDoll
  • 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
  • anonymous
Not sure how to combine the middle terms but I know they are both \[-2\sqrt{a+1}\]
UsukiDoll
  • 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
  • UsukiDoll
yeah ...we're supposed to have -4\sqrt{a+1}
UsukiDoll
  • UsukiDoll
I would ignore the a+1 in the square root part and just compute -2-2
Jhannybean
  • Jhannybean
\[-2ab \rightarrow -2(\sqrt{a+1})(2)\] in correctingmy error.
anonymous
  • 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
  • Jhannybean
That looks correct
anonymous
  • anonymous
Oh my gosh wow it took me a long time but I got 100% XD
UsukiDoll
  • UsukiDoll
\[a+1-2\sqrt{a+1}-2\sqrt{a+1}+4 \rightarrow \frac{a-4\sqrt{a+1}+5}{a-3}\]
anonymous
  • anonymous
Thanks
UsukiDoll
  • UsukiDoll
yup it's correct XD
anonymous
  • anonymous
I'm still way behind on summer school but oh well lol
UsukiDoll
  • UsukiDoll
ouch. how much more material do you have to complete?
anonymous
  • anonymous
I'm three percent done and I need to be 100% by August 1 XD
anonymous
  • anonymous
Plus I need to be 100% done on another class too by that time
anonymous
  • anonymous
So it's gonna be crunch time XD
UsukiDoll
  • UsukiDoll
oh. time for all nighters. Drink tons of coffee!
anonymous
  • anonymous
Yup
UsukiDoll
  • 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
  • anonymous
Good plan I'll just get 20% done a day and I'll be done just on time XD

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