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Math Help - Show work by using + and - on a number line

  1. #1
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    Show work by using + and - on a number line

    I know how to find domains, but this instruction on the method to do it with confused me. I remember my teacher doing a long series of + and - symbols placed vertically below a number line, but I'm not sure how she did it. The problem I am supposed to find the domain of is:

    2x X > 3X
    _____ + _ _________
    ______
    2 2 2
    X -4 X +X-6 X + 5X + 6

    Any help would be appreciated. Thanks.
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  2. #2
    MHF Contributor

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    Quote Originally Posted by cheeseokay View Post
    I know how to find domains, but this instruction on the method to do it with confused me. I remember my teacher doing a long series of + and - symbols placed vertically below a number line, but I'm not sure how she did it. The problem I am supposed to find the domain of is:

    2x X > 3X
    _____ + _ _________
    ______
    2 2 2
    X -4 X +X-6 X + 5X + 6

    Any help would be appreciated. Thanks.
    The first thing you need to do is get that \frac{3x}{x^2+ 5x- 6} on the left so you have \frac{2x}{x^2- 4}+ \frac{x}{x^2+ x- 6}- \frac{3x}{x^2+ 5x+ 6}\ge 0.

    Now add the fractions on the left getting the common denominator. Fortunately, that's not too hard since those denominators have similar factors.
    Now, determine where the numerators are 0 (that's easy: x= 0) and where the denominators are 0 (a little harder: solve that polynomial to 0 and factor it. Fortunately, you determined the factors when you formed the common denominator!

    The points where the numerator or denominator are 0 separate "+" from "-". The simplest way to figure which is correct for an integerval is to look at the individual factors. An odd number of - factors, negative, and even number of - factors, positive. Also note that as you "step over" x= a, the term x- a is the only one that changes sign.
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  3. #3
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    Thanks for the help! I did get that question right, but I have a couple more things to ask you. What did your last sentence mean? What's x=a? What's "stepping over?"
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