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Homework Help: Solve For X

  1. Dec 8, 2004 #1
    I tried to do this problem soo many times but cant even get close to the answer, I dont know what to do.

    [(x)/(x-2)]+2=[(5x)/(x+2)]+[(3x+1)/(x^(2)-4)]

    ok I know the LCD is (x+2)(x-2) and that x^(2)-4 is a perfect square that can be written as (x-2) (x+2)

    But I cant get the solution it says x=3, 3/2

    PLEASE HELP ME SOMEONE :confused:
     
  2. jcsd
  3. Dec 8, 2004 #2
    dear aisha

    just make sure that the denominator is equal to x²-4 everywhere...
    then you can forget about it (ofcourse x can't be 2 or -2)


    like this :

    [(x)(x+2)+2(x²-4)=[(5x)(x-2)+[(3x+1)]

    Then solve for x...

    can you go on from here ???

    regards
    marlon
     
  4. Dec 8, 2004 #3

    Diane_

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    Homework Helper

    If you multiply through by the LCD, you'll get:

    (x/(x-2))(x-2)(x+2) + 2(x^2-4) = (5x/(x+2))(x-2)(x+2) + ((3x+1)/(x^2-4))(x+2)(x-2)

    Simplifying gives you

    x(x+2) + 2(x^2 - 4) = 5x(x-2) + (3x+1)

    Multiply it out, collect similar terms, and you'll have a quadratic. That can be factored, or you can use the Quadratic Formula. Don't forget to distribute minus signs.

    Does that help?
     
  5. Dec 8, 2004 #4
    YES THAT HELPS, BUT The quadratic formula I got after multiplied out and collected the like terms was -2x^(2)-x+1 and this factored out and x=-1/2 or x=-1 but the solutions were x=3, 3/2 am I wrong or is the solution wrong?
     
  6. Dec 8, 2004 #5

    Diane_

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    Homework Helper

    I think you're off somewhere. The quadratic I ended up with was

    2x^2 - 9x + 9 = 0

    which has the "proper" solutions. It's probably a simple math error. Go back through it and check it.

    Unsolicited advice: I have found that students often make those little errors because they're trying to go too fast. I know that the grunt work of algebra can be snore-inducing, but you need to take it slowly at first. Speed comes with experience, and experience is what you're lacking right now. You'll get there, though. All it takes is time. :) </mommy-mode>
     
  7. Dec 8, 2004 #6
    Thanks Diane I got it FINALLY :smile:
     
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