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Math Help - Need help with an equation based on quadratic formula

  1. #1
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    Need help with an equation based on quadratic formula

    I have the following problem and I've been trying to solve it

    \frac{6}{r^2-1}-\frac{1}{2}=\frac{1}{r+1}

    but when I try solving I just can't figure out how they get to 3 and -5. I'm supposed to solve it turning it into

     ax^2+bx+c=0

    I need to get rid of these denominators and therefore multiply the whole expression by its least common denominator

     2(r^2-1)(r+1)

    but I stay stucked...!! Need guidance.
    Last edited by Alienis Back; October 22nd 2010 at 05:03 AM.
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  2. #2
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    you're probably confusing signs... try to take 1/r+1 to the ledtside and 1/2 to the right, the factorise 1/r+1 and derive the quadratic equation ...what do you get?
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  3. #3
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    Note that r^2-1 = (r-1)(r+1) (difference of two squares)

    This means that the denominator is r^2-1

    \dfrac{6}{r^2-1} - \dfrac{1}{2} \cdot \dfrac{(r^2-1)}{r^2-1} = \dfrac{r-1}{r^2-1}

    Then multiply by 2 to get \dfrac{12}{r^2-1} - \dfrac{(r^2-1)}{r^2-1} = \dfrac{2(r-1)}{r^2-1}

    The denominator will cancel and then should be easy to simplify and solve - just remember that r \neq \pm 1 as this would entail division by 0
    Last edited by e^(i*pi); October 22nd 2010 at 07:44 AM. Reason: making the working clearer
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  4. #4
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    Haven't found my way yet

    I did what you said but cannot find the x = 3 , -5 yet. Can anyone please tell me where my mistake is?Need help with an equation based on quadratic formula-excercise.pdf
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  5. #5
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    Quote Originally Posted by Alienis Back View Post
    \frac{6}{r^2-1}-\frac{1}{2}=\frac{1}{r+1}
    Start this way (easier LCM):
    6 / (r^2 - 1) = 1 / (r + 1) + 1/2 ; combine right side:
    6 / (r^2 - 1) = (r + 3) / [2(r + 1)] ; factor left side:
    6 / [(r + 1)(r - 1)] = (r + 3) / [2(r + 1)] ; cancel out the (r + 1)'s:
    6 / (r - 1) = (r + 3) / 2 ; crossmultiply:
    (r - 1)(r + 3) = 12 ; expand left side:
    r^2 + 2r - 3 = 12

    Can you wrap it up? I'm sure you can.
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