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Math Help - difficulty with quadratic fraction problem

  1. #1
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    difficulty with quadratic fraction problem

    Hello all. i'm currently trying to solve this equation:

    x-1 / x - 4 / x+3 = 0


    my skills with rational equations are very limited, and find myself getting getting frustratingly confused alot !

    i've got as far as :

    (x-1)(x+3) / x(x+3) - 4x / x(x+3)



    i'm hoping someone can give me some insight into solving this as i'm lost as to what i need to do next.


    Cheers
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  2. #2
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    e^(i*pi)'s Avatar
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    If it's \dfrac{x-1}{x} + \dfrac{4}{3} = 0

    Multiply through by the lowest common denominator and simplify the linear equation you're left with

    Do you know what the LCD is?
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  3. #3
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    Hi there, well in terms of my equation, i've got the LCD as x(x+3) . see my original post, is this so far so good?

    kind thanks
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  4. #4
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    So your equation is \frac{x- 1}{x}- \frac{4}{x+ 3}= 0?

    Yes, the LCD is x(x+3). Multiply each part of the equation by that and you will get rid of the fractions.
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  5. #5
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    ok i shall crack on with that. many thanks!
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  6. #6
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    hello once again.. ok, i feel i've moved on a little bit with this but seemingly got stuck again as i cant seem to get a quadratic form..

    so i've muliplied by x(x+3) to give:

    x-1(x(x+3)) / x - 4(x(x+3)) / (x+3)

    cancelling i then get:

    x-1(x+3) - 4x

    expanding :

    x - x - 3 - 4x ...

    i'm lost! help appreciated. thanks in advance.
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  7. #7
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    just to re-iterate, the original equation was:


    x-1 / x - 4 / x+3 = 0
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  8. #8
    Junior Member BobBali's Avatar
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    After you canceld out the denominators with LCD x(x+3) we get>

    [tex](x+3)(x+1) - 4x = 0 [\math]

    [tex] x^2 - x + 3x - 3 - 4x = 0 [\math]

    [tex] x^2 -2x -3 = 0 [\math]

    Now factorize > [tex] (x -3) (x +1) = 0 [\math]

    Therefore, x=3 and x=-1
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  9. #9
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    Thankyou very much. after some reworking to get how it should look, i can see where i was going wrong now!
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