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Math Help - Dividing Rational Expressions!

  1. #1
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    Dividing Rational Expressions!

    Please help with this prob. It is over fifty and I cant finish it all by my self in just 8 hours time so can anybody help me with this 15 items of expressions?

    here are they:


    2a+2b__________ a^2-b^2
    ------ Divided by ---------
    a^2__________ 4a

    ____________________________

    a^2-4__________ a^2-a-2
    ------ Divided by ----------
    a^2-1__________ a^2+a-2


    ____________________________

    4a^2-25 ________ 12a+30
    -------- Divided by---------
    a^2-16 ________ 2a^2+8a


    ____________________________

    a^4-b^4________ a^2+b^2
    -------- Divided by---------
    5a-5b___________ 5


    ___________________________

    a^2-b^2
    --------- Divided by a+b
    a^2+b^2
    Last edited by Hardheaded; October 15th 2006 at 05:48 AM. Reason: typo
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  2. #2
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    ^^^ Continuation

    x^2-13x+42_________ 2x^2-13x-7
    ----------- Divided by------------
    6+x-x^2____________ 2x^2-5x-3


    ______________________________________

    x^2+2x^2________ 1-4x^2
    ----------Divided by----------
    9-x^2____________3x+2x^2


    ______________________________________

    a^3-ab^3_________a^2+ab
    ----------Divided by------------
    a^2b_____________3ab+3b^2


    ______________________________________

    a^4-b^4_________2a^2+2b^2
    ---------Divided by------------
    3a+3n_______________6


    ______________________________________

    m^2-3m+2___________2-m
    -----------Divided by--------
    m^2-1______________1-m


    ______________________________________


    2a^2-11a+12_________a^3+4a^2
    -------------Divided by------------
    27-18a_______________6a^3-96a


    ______________________________________

    1___________ 1___________1
    ---Dividedby-----Divided by-----
    xy_________xy^2________x^2y


    ______________________________________

    _2x-7_____________7-2x
    ( ----)^2 Dividedby (----)^4
    __9________________3


    ______________________________________

    6x^2_________21________x^2
    -----dividedby----dividedby----
    6x-14_______9x-21_______35


    ______________________________________

    x^2____________x+y__________x
    --------dividedby-----dividedby(----)^2
    x^2-y^2________x-y__________x+y


    ______________________________________



    Thanks for the ones who can help ;-)

    Sincerely,

    Hardheaded


    *note: this (^) symbolizes that the number at the right of it is raised
    ______and n symbolizes that all nos. inside the pharenthese is raised
    (-----)^2
    m



    one again,


    THANKS!
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  3. #3
    Senior Member OReilly's Avatar
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    Quote Originally Posted by Hardheaded View Post
    Please help with this prob. It is over fifty and I cant finish it all by my self in just 8 hours time so can anybody help me with this 15 items of expressions?

    here are they:


    2a+2b__________ a^2-b^2
    ------ Divided by ---------
    a^2__________ 4a

    ____________________________

    a^2-4__________ a^2-a-2
    ------ Divided by ----------
    a^2-1__________ a^2+a-2


    ____________________________

    4a^2-25 ________ 12a+30
    -------- Divided by---------
    a^2-16 ________ 2a^2+8a


    ____________________________

    a^4-b^4________ a^2+b^2
    -------- Divided by---------
    5a-5b___________ 5


    ___________________________

    a^2-b^2
    --------- Divided by a+b
    a^2+b^2
    I will do just first problem because I really can't write without LaTex, someone else on forum will help you with others:

    1)
    [(2a+2b)/a^2] / [(a^2-b^2)/4a] = [2(a+b)/a^2] * [4a/[(a+b)(a-b)]] =
    8/(a^2-ab)
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  4. #4
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    Help

    Can anybody answer the remaining items?




    Please I desperately need it!
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Hardheaded View Post
    a^2-4__________ a^2-a-2
    ------ Divided by ----------
    a^2-1__________ a^2+a-2
    I think, rather than try to have someone do all these for you, it would be better to have someone explain what needs to be done.

    So, the first thing you need to do with problems like these is factor whatever you can in the numerators and denominators. Then you cancel what you can.

    The hardest part of this problem is the factoring, so let's look at the kinds of factoring problems you have here.

    First:
    a^2 - 4
    This is of the form of the difference between two squares:
    a^2 - b^2 = (a+b)(a-b)
    So
    a^2 - 4 = (a+2)(a-2)

    a^2 - 1 is similar: a^2 - 1 = (a+1)(a-1)

    Now we are left with a^2 - a - 2 and a^2 + a - 2. Typically you can guess at these:
    a^2 - a - 2 = (a + _)(a + _)
    The missing numbers must be factors of -2 of which there are only 4. So there are only a small number of possibilities here:
    (a + 2)(a - 1) = a^2 + a - 2
    (a + 1)(a - 2) = a^2 - a - 2
    (The other combinations just repeat these factors in a different order.)

    As it happens, in the process we also managed to factor a^2 + a - 2.

    So the problem, after all the factoring has been done, becomes:
    (a+2)(a-2)(a+1)(a-2)
    (a+1)(a-1)(a+2)(a-1)

    Cancelling the common factors we get:

    (a-2)^2
    (a-1)^2

    All of these problems are done in exactly the same way. Since the only problem I can imagine you would have with these would be factoring, what I would suggest is that you go through these and factor what you can factor. Then make a list of what you are having problems factoring and post those. That would make it much more simple for all of us to help you where you most need it.

    -Dan
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