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Math Help - Inequalities problems

  1. #1
    Junior Member
    Joined
    Feb 2011
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    55

    Inequalities problems

    Could someone point out what I'm doing wrong here please:

    \frac{3}{x+1} <\frac{2}{x}

    \frac{3}{x+1} - \frac{2}{x} <0

    \frac{x-2}{x(x+1)} <0

    From there I know that the function =0 when x=2
    So I know that the function is less than 0 when x<2
    But this is wrong according to the answers.

    Help appreciated!
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  2. #2
    MHF Contributor
    Joined
    Dec 2009
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    Thanks
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    Re: Inequalities problems

    Quote Originally Posted by elieh View Post
    Could someone point out what I'm doing wrong here please:

    \frac{3}{x+1} <\frac{2}{x}

    \frac{3}{x+1} - \frac{2}{x} <0

    \frac{x-2}{x(x+1)} <0

    From there I know that the function =0 when x=2
    So I know that the function is less than 0 when x<2
    But this is wrong according to the answers.

    Help appreciated!
    Looking at your final fraction, it is less than zero for positive divided by negative
    or for negative divided by positive,
    so you have a few cases to examine.

    The numerator is negative for x < 2,
    but the denominator is positive for x and x+1 both positive or both negative.

    Similarly, the numerator is positive for x > 2
    and the denominator is always positive in this case.

    Hence we cannot have positive divided by negative for this fraction.
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  3. #3
    Junior Member
    Joined
    Feb 2011
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    55

    Re: Inequalities problems

    Completely forgot about the denominator!
    Thanks.
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