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anonymous

  • one year ago

More help on algebra please?

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  1. anonymous
    • one year ago
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    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.

  2. UsukiDoll
    • one year ago
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    sigh it's nice to know that someone is doing latex.. it sucks that my fraction latex is broken .

  3. anonymous
    • one year ago
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    latex?

  4. UsukiDoll
    • one year ago
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    \[\frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}+2 } \cdot \frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}-2 } \]

  5. UsukiDoll
    • one year ago
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    yeah that's used to type Math. It's called Latex. But on my end it's coo coo

  6. anonymous
    • one year ago
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    Ohh

  7. UsukiDoll
    • one year ago
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    \[\frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}+2 } \cdot \frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}-2 } \rightarrow \frac{(\sqrt{a+1}-2)(\sqrt{a+1}-2)}{(\sqrt{a+1}+2)(\sqrt{a+1}-2)}\]

  8. UsukiDoll
    • one year ago
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    can we not give direct answers please? It's against code of conduct

  9. LilyMQ
    • one year ago
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    oh sorry I'm new here

  10. LilyMQ
    • one year ago
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    deleted

  11. UsukiDoll
    • one year ago
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    ah. I see. Ok.

  12. anonymous
    • one year ago
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    @LilyMQ I do need to know how

  13. UsukiDoll
    • one year ago
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    You can read more about the code of conduct here. http://openstudy.com/code-of-conduct

  14. UsukiDoll
    • one year ago
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    anyway where was I? \[\frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}+2 } \cdot \frac{ \sqrt{a+1}-2 }{ \sqrt{a+1}-2 } \rightarrow \frac{(\sqrt{a+1}-2)(\sqrt{a+1}-2)}{(\sqrt{a+1}+2)(\sqrt{a+1}-2)}\]

  15. UsukiDoll
    • one year ago
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    so we need to use the foil method... as usual the denominator is always easier because the middle terms are cut out

  16. UsukiDoll
    • one year ago
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    \[\frac{(\sqrt{a+1}-2)(\sqrt{a+1}-2)}{(\sqrt{a+1}+2)(\sqrt{a+1}-2)} =\frac{?}{(a+1)-4}\]

  17. UsukiDoll
    • one year ago
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    so foil is needed on the numerator .

  18. UsukiDoll
    • one year ago
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    our denominator should be a+1-4=a-3

  19. UsukiDoll
    • one year ago
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    dear gawd latex... U SUCK! |dw:1437556072647:dw|

  20. anonymous
    • one year ago
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    Ok I'm following

  21. UsukiDoll
    • one year ago
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    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 \[\ \frac{\sqrt{a+1} \sqrt{a+1}-2 \sqrt{a+1}-2 \sqrt{a-1}+(-2)(-2)}{a-3}\]

  22. UsukiDoll
    • one year ago
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    -_-

  23. anonymous
    • one year ago
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    It actually looks fine on my side

  24. Jhannybean
    • one year ago
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    Yeah same here |dw:1437556324233:dw|

  25. anonymous
    • one year ago
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    Ok so we end up with \[a+1-2\sqrt{a+1}-2\sqrt{a+1}+4\] but I'm not sure?

  26. Jhannybean
    • one year ago
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    Remember your polynomial expansion : \((a-b)^2 = a^2 -2ab+b^2\)

  27. Jhannybean
    • one year ago
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    And take \(a= \sqrt{a+1}\) and \(b = -2\)

  28. UsukiDoll
    • one year ago
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    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

  29. anonymous
    • one year ago
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    Not sure how to combine the middle terms but I know they are both \[-2\sqrt{a+1}\]

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

  31. UsukiDoll
    • one year ago
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    yeah ...we're supposed to have -4\sqrt{a+1}

  32. UsukiDoll
    • one year ago
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    I would ignore the a+1 in the square root part and just compute -2-2

  33. Jhannybean
    • one year ago
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    \[-2ab \rightarrow -2(\sqrt{a+1})(2)\] in correctingmy error.

  34. anonymous
    • one year ago
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    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 \[\frac{ 5+a-4\sqrt{a+1} }{ a-3 }\]

  35. Jhannybean
    • one year ago
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    That looks correct

  36. anonymous
    • one year ago
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    Oh my gosh wow it took me a long time but I got 100% XD

  37. UsukiDoll
    • one year ago
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    \[a+1-2\sqrt{a+1}-2\sqrt{a+1}+4 \rightarrow \frac{a-4\sqrt{a+1}+5}{a-3}\]

  38. anonymous
    • one year ago
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    Thanks

  39. UsukiDoll
    • one year ago
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    yup it's correct XD

  40. anonymous
    • one year ago
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    I'm still way behind on summer school but oh well lol

  41. UsukiDoll
    • one year ago
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    ouch. how much more material do you have to complete?

  42. anonymous
    • one year ago
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    I'm three percent done and I need to be 100% by August 1 XD

  43. anonymous
    • one year ago
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    Plus I need to be 100% done on another class too by that time

  44. anonymous
    • one year ago
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    So it's gonna be crunch time XD

  45. UsukiDoll
    • one year ago
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    oh. time for all nighters. Drink tons of coffee!

  46. anonymous
    • one year ago
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    Yup

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

  48. anonymous
    • one year ago
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    Good plan I'll just get 20% done a day and I'll be done just on time XD

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