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Math Help - Reducing to lowest terms(rational expression)

  1. #1
    Newbie
    Joined
    Oct 2006
    Posts
    5

    Reducing to lowest terms(rational expression)

    Hello I'm new here, and can you help me with this problem.

    I will be reporting these rational expression tommorow but I have limited time, I'm busy at all my other homeworks and I am trying to complete my science investigatory project today so please help me?

    Here are the expressions:

    ( ONE )

    a^2 + 4ab + 4b^2
    ------------------
    a^2 - 4b^2
    __________________________________________________ ____________________
    ( TWO )

    9x^2 + 6xy + y^2
    ------------------
    9x^2 - y^2

    __________________________________________________ ____________________
    ( THREE )

    4a + 4
    ------------------
    a^2 + 2a + 1

    __________________________________________________ ____________________
    ( FOUR )

    6x + 12
    ------------------
    x^2 + 4x + 4

    __________________________________________________ ____________________
    ( FIVE )

    6x^2 - 6
    ------------------
    (x-1)^2

    __________________________________________________ ____________________
    ( SIX )

    5x^2 - 20
    ------------------
    2x - 4

    __________________________________________________ ____________________
    ( SEVEN )

    x^2 - 16
    ------------------
    2x + 8

    __________________________________________________ ____________________
    ( EIGHT )

    x^2 - 2x -3
    ------------------
    x^2 - 9

    __________________________________________________ ____________________
    ( NINE )

    x^2 - 5x + 4
    ------------------
    x^2 - 1
    __________________________________________________ ____________________
    ( TEN )

    2x^2 + x - 6
    ------------------
    x^2 + x - 2



    note: the symbol (^) denots that the no. on the right side of it is raised.

    Thank you to everyone who can help
    Last edited by Hardheaded; October 4th 2006 at 05:49 AM. Reason: So that people wont be confussed
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  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
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    Hello, Hardheaded!

    Welcome aboard!

    These are all of the same type.
    You are expected to know how to factor and reduce.
    I'll do a few to get you started . . .



    . . . a + 4ab + 4b
    1) . ------------------
    . . . . . a - 4b

    . . . . . . .(a + 2b)(a + 2b)
    Factor: . --------------------
    . . . . . . .(a - 2b)(a + 2b)

    . . . . . . . a + 2b
    Reduce: . --------
    . . . . . . . a - 2b



    . . . . . 4a + 4
    3) . --------------
    . . . a + 2a + 1

    . . . . . . . . .4(a + 1)
    Factor: . -----------------
    . . . . . . .(a + 1)(a + 1)

    . . . . . . . . .4
    Reduce: . -------
    . . . . . . . .a + 1




    . . . 5x - 20
    6) . -----------
    . . . . 2x - 4

    . . . . . . .5(x - 4) . . . . 5(x - 2)(x + 2)
    Factor: . ----------- . = . -----------------
    . . . . . . .2(x - 2) . . . . . . . 2(x - 2)

    . . . . . . . 5(x + 2)
    Reduce: . ----------
    . . . . . . . . . .2

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  3. #3
    Senior Member OReilly's Avatar
    Joined
    Mar 2006
    Posts
    340
    I will do the rest that Soroban didn't do.

    2)

    9x^2 + 6xy + y^2
    ------------------ =
    9x^2 - y^2

    (3x+y)(3x+y)
    ------------ =
    (3x-y)(3x+y)

    3x+y
    ----
    3x-y


    4)
    6x + 12
    --------------- =
    x^2 + 4x + 4

    6(x+2)
    ----------- =
    (x+2)(x+2)

    6
    ----
    x+2


    5)

    6x^2 - 6
    ---------- =
    (x-1)^2

    6(x^2 - 1)
    --------- =
    (x-1)(x-1)

    6(x-1)(x+1)
    ----------- =
    (x-1)(x-1)

    6(x+1)
    ------
    x-1


    7)

    x^2 - 16
    ----------- =
    2x + 8

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

    x-4
    ---
    2

    8)

    x^2 - 2x -3
    ------------- =
    x^2 - 9

    (x+1)(x-3)
    ---------- =
    (x-3)(x+3)

    x+1
    ---
    x+3


    9)
    x^2 - 5x + 4
    -------------- =
    x^2 - 1

    (x-1)(x-4)
    ---------- =
    (x-1)(x+1)

    x-4
    ---
    x+1


    10)
    2x^2 + x - 6
    ------------- =
    x^2 + x - 2

    (2x-3)(x+2)
    ----------- =
    (x-1)(x+2)

    2x-3
    ----
    x-1
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  4. #4
    Newbie
    Joined
    Oct 2006
    Posts
    5
    thank you thank you thank you!


    thanks for the help
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