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Math Help - Algebra problem.... me again

  1. #1
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    Algebra problem.... me again

    The problem is


    2 + (1 / y + 1) - (1 / y - 1) = 0


    Ok what I did was Mulitply the entire equation by the common denominator of

    (y + 1)(y - 1).

    I end up getting


    2(y + 1)(y - 1) + y - 1 - y + 1 = 0

    From here, I keep working the problem until it gets to

    2(y^2 - 1) = 0

    2y^2 - 2 = 0

    (2y^2 - 2) / 2

    y^2 - 1 = 0

    y^2 = 1

    Square root both sides to get

    y = +- 1

    The problem is, when entering either one of these solutions into the original problem, i'm always getting one of the divisions within the problem where the denominator is 0 and that is undefined....so i'm kinda lost. Is there no solution or?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by JonathanEyoon View Post
    2(y + 1)(y - 1) + y - 1 - y + 1 = 0
    you made a mistake in this line:

    it is, 2(y + 1)(y - 1) + (y - 1) - (y + 1) = 0

    => 2(y + 1)(y - 1) + y - 1 - y - 1 = 0
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    you made a mistake in this line:

    it is, 2(y + 1)(y - 1) + (y - 1) - (y + 1) = 0

    => 2(y + 1)(y - 1) + y - 1 - y - 1 = 0


    DOH!!! thanks for pointing that out


    So the end solution should instead be

    Y = +- Squareroot of 2
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by JonathanEyoon View Post
    DOH!!! thanks for pointing that out


    So the end solution should instead be

    Y = +- Squareroot of 2
    yes
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  5. #5
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    Quote Originally Posted by Jhevon View Post
    yes



    MmMm.... how would I punch that into a Ti-83 calculator to double check? I'm putting it into the calculator like this


    2 + (1 / (squareroot 2) + 1) - (1 / (squareroot 2) - 1

    The answer comes out to 4 instead of 0 for both postive and negative squareroot of 2.
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by JonathanEyoon View Post
    MmMm.... how would I punch that into a Ti-83 calculator to double check? I'm putting it into the calculator like this


    2 + (1 / (squareroot 2) + 1) - (1 / (squareroot 2) - 1

    The answer comes out to 4 instead of 0 for both postive and negative squareroot of 2.
    you forgot the last bracket. it should be:

    2 + (1 / ((squareroot 2) + 1)) - (1 / ((squareroot 2) - 1))

    i punched it into my regular scientific calculator and got 0
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  7. #7
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    Quote Originally Posted by Jhevon View Post
    you forgot the last bracket. it should be:

    2 + (1 / ((squareroot 2) + 1)) - (1 / ((squareroot 2) - 1))

    i punched it into my regular scientific calculator and got 0


    You are awesome!
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