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Math Help - Algebraic fractions

  1. #1
    Junior Member Turple's Avatar
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    Question Algebraic fractions

    I'm just confused about a couple of rules. For example if I have multiplied a fraction out to get 9(x+4)-2(x+2) does the 2 in the second bracket get multiplied by -2 or 2?

    Also if I have this: 2(x+4)(x+2) is it only the x+4 which is doubled? Or do you work out the quadratic and multiply the whole thing by two?

    Thanks
    Last edited by Turple; May 13th 2008 at 10:01 PM.
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  2. #2
    Moo
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    Hello,

    Quote Originally Posted by Turple View Post
    I'm just confused about a couple of rules. For example if I have multiplied a fraction out to get 9(x+4)-2(x+2) does the 2 in the second bracket get multiplied by -2 or 2?
    -2

    Also if I have this: 2(x+4)(x+2) is it only the x+4 which is doubled? Or do you work out the quadratic and multiply the whole thing by two?

    Thanks
    2(x+4)(x+2)=[2(x+4)](x+2)=2[(x+4)(x+2)]=(x+4)[2(x+2)]

    So it's both of them
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  3. #3
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    Quote Originally Posted by Turple View Post
    ...

    I also can't understand how to work out these fractions:

    2x ...... 9
    ---- - ---- = 2
    x+4 ........ x+2


    ...
    I'm going to show you the first example step by step. The following examples can be solved in exactly the same way:

    1. Domain: The denominator must be unequal to zero. Therefore

    D=\mathbb{R}\setminus \{-4, -2\}

    2. The common denominator of the fractions is (x+4)(x+2). Change the fractions so they have both the same denominator:

    \frac{2x (x+2)}{(x+4)(x+2)} - \frac{9 (x+4)}{(x+4)(x+2)} = 2

    3. Multiply both sides of the equation by the common denominator to get rid of the fractions:

    2x(x+2)-9(x+4)=2(x+4)(x+2)

    4. Expand all brackets:

    2x^2+4x-9x-36=2(x^2+6x+8)

    5. Collect like terms:

    2x^2-5x-36=2x^2+12x+16

    -17x=52

    6. Divide by the leading factor of x:

    \boxed{x=-\frac{52}{17}}
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