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Math Help - Please Help with this problem 3/x-4=5/x ??????

  1. #1
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    howell
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    Please Help with this problem 3/x-4=5/x ??????

    Please help me
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  2. #2
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    Re: Please Help with this problem 3/x-4=5/x ??????

    You should state your problem more clearly with correct Order of Operation symbols because the "3/x-4" part can be either recognized as "3 / (x-4)" or "(3/x) - 4"

    But anyway for "3 / (x-4)" I cross multiplied and got 3x = 5(x - 4) and use the distributive property on the right side to get 3x = 5x - 20
    Then I subtract 5x from both sides and end up with -2x = -20
    Divide both sides by -2 and get x = 10

    For "(3/x) - 4" I first found a common denominator for the lone '4' by multiplying its denominator (invisible '1') by x and multiplying the numerator as well to get '4/x' so the equation looks like: (3/x) - (4x/x) = 5/x
    Then I combined the left side to get (3 - 4x) / x = 5/x
    Then I cross-multiply again to get: x(3 - 4x) = 5x
    Use distributive property on the left side to get: 3x - 12x^2 = 5x
    Looks like a quadratic equation so I move everything over to one side: 12x^2 + 5x - 3x = 0
    Then use the quadratic formula to get the solutions: x = 1/3 or x = -3/4

    Be sure to check those answers
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  3. #3
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    howell
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    Re: Please Help with this problem 3/x-4=5/x ??????

    Thank you very much. I meant to do this 3 / (x-4).
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