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Math Help - simplify

  1. #1
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    simplify

    Question is simplify the following expression

    1 _ 1
    x+2 x+4
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  2. #2
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    Quote Originally Posted by kiwisa View Post
    Question is simplify the following expression

    1 _ 1
    x+2 x+4
    I assume the expression is \displaystyle {\frac{1}{x + 2} + \frac{1}{x + 4}}.

    First try to tell me this: How you would simplify \displaystyle {\frac{1}{3} + \frac{1}{5}} ? Show every step.
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  3. #3
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    sorry but the minus sign merged with the line in the fraction so it is the 2 fractions minus each other.

    1/3 + 1/5

    1x5/3x5 +1x3/5x3

    5/15 + 3/15

    8/15
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  4. #4
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    Quote Originally Posted by kiwisa View Post
    sorry but the minus sign merged with the line in the fraction so it is the 2 fractions minus each other.

    1/3 + 1/5

    1x5/3x5 +1x3/5x3

    5/15 + 3/15

    8/15
    Good. Now try to do the same thing with the expression you posted (but use a minus sign). Show every step.
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  5. #5
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    1/x+2 - 1/x+4

    1x2/x+2x2 - 1/x+4

    2/x+4 - 1/x+4

    1/x+4
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  6. #6
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    Quote Originally Posted by kiwisa View Post
    1/x+2 - 1/x+4

    1x2/x+2x2 - 1/x+4

    2/x+4 - 1/x+4

    1/x+4
    That's not valid! x + 2 can be thought of as a single number that is dividing into 1, and if you are multiplying the 2 by 2, you have to multiply the x by 2 as well.

    2(x + 2) = x2 + 4

    Maybe if you substituted x + 2 and x + 4 as a single variable, you will see how your method was wrong and you will also see the correct way to solve this problem:
    j = x + 2
    v = x + 4
    \frac{1}{j} - \frac{1}{v}
    Simplify this just like you did the example, and at the end, put in the true values of j and v back in.
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  7. #7
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    Now I am really lost, I can see what you are saying regarding the whole fraction been multiplied so it should read 2/2x+4, but then what?
    Last edited by kiwisa; July 16th 2010 at 06:18 PM. Reason: edited words
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  8. #8
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    1 / x+4(x+2) - 1 /x+2(x+4)

    x + 4 / (x^2 + 6x + 8) - [ x + 2 / (x^2 + 6x + 8) ]

    [x + 4 - ( x + 2 )] / x^2 + 6x + 8

    2 / x^2 + 6x + 8
    Last edited by Zharif93; July 16th 2010 at 06:48 PM.
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  9. #9
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    ok so where does the 6x come from? I can see where the x^2 and the 8 come from. Sorry i just dont get this stuff.
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  10. #10
    Senior Member eumyang's Avatar
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    It comes from FOILing (x + 4)(x + 2):
    (x + 4)(x + 2) = x^2 + 2x + 4x + 8 = x^2 + 6x + 8
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  11. #11
    Newbie Zharif93's Avatar
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    ( x + 4 ) ( x + 2 )

    X x X + X x 2 + X x 4 + 8

    x ^ 2 + 2x + 4x + 8

    x ^ 2 + 6x + 8
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  12. #12
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    Thanks i get that now
    Last edited by mr fantastic; July 16th 2010 at 07:14 PM. Reason: Tagged question moved to new thread.
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  13. #13
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    Quote Originally Posted by Zharif93 View Post
    1 / x+4(x+2) - 1 /x+2(x+4)

    x + 4 / (x^2 + 6x + 8) - [ x + 2 / (x^2 + 6x + 8) ]

    [x + 4 - ( x + 2 )] / x^2 + 6x + 8

    2 / x^2 + 6x + 8
    I think you meant:

    (x + 4)/(x+4)(x+2) - (x + 2)/(x+2)(x+4)

    = (x + 4)/ (x^2 + 6x + 8) - [(x + 2) / (x^2 + 6x + 8) ]

    = [x + 4 - ( x + 2 )] /(x^2 + 6x + 8)

    = 2 / (x^2 + 6x + 8)
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