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Math Help - Equation Help

  1. #1
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    Equation Help

    I'm having a bit of trouble with this problem.

    Solve the equation.
    3/2x-1/x+1=1/x(3x+3)

    Here is an image of the problem if the equation above is not clear
    http://i1198.photobucket.com/albums/...g?t=1297473401
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  2. #2
    A Plied Mathematician
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    Is this for an online quiz?
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  3. #3
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    No, just practice.
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  4. #4
    A Plied Mathematician
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    Ok, that's fine. What ideas have you had so far?
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  5. #5
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    Clearing out the denominators by multiplying the whole equation by (2x) (x+1) x(3x+3)
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  6. #6
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    Go for it; that idea sounds good. Post what you get, and we can help you from there.
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  7. #7
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    After multiplying by (2x) (x+1) x(3x+3) and simplifying I get 3x^3+12x^2+9x=2x^2+2x. This is the part where I'm sort of lost; I'm not sure if I made a mistake or not.
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  8. #8
    A Plied Mathematician
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    No mistakes so far. Notice that every single term has an x in it. Since x = 0 is not a solution of the original equation (you'd divide by zero in the first term!), you can cancel a power of x from every term. What do you suppose you could do next?
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  9. #9
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    By canceling a power of x from every term do you mean just taking an x out of every term? So 3x^3-10x^2+7x=0 would be 3x^2-10x+7=0?
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  10. #10
    A Plied Mathematician
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    Exactly. Then what?
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  11. #11
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    Could I use the quadratic equation at this point?
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  12. #12
    A Plied Mathematician
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    Sure, why not? What's the result?
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  13. #13
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    Using the quadratic equation and substituting 3=a, -10=b and 7=c I get x=7/3 and x=6/6 (1)
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  14. #14
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    I think your answers are off by a minus sign. If you're ever in doubt, plug your solutions back into the equation and see if they satisfy it.
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  15. #15
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    Using 3x^2-10x+7 in the quadratic formula I get x= 10(plus or minus) 4/6 Is that right or did I make a mistake before that?
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