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Thread: Factoring Help

  1. #1
    Newbie
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    Sep 2007
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    2

    Factoring Help

    I need some help on some problems.

    1. $\displaystyle 25-10a+a^2-y^2
    $

    2.
    $\displaystyle y^2-4x^2-20x-25
    $

    3.
    $\displaystyle x^2+2
    $
    ______
    $\displaystyle x
    $

    4.
    $\displaystyle 4y(y-3)^3(y+4)^4+6y(y-3)^5(y+4)^2
    $

    5.
    1.. 1
    - + -
    x.. 2

    6.
    3x.. 1.. 1
    -- + - = -x - 2
    4... 2.. 3

    7.
    .x......3x
    ---. = ---
    x+2....x-1
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  2. #2
    MHF Contributor red_dog's Avatar
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    Medgidia, Romania
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    5
    1. $\displaystyle 25-10a+a^2-y^2=(5-a)^2-y^2$ and use $\displaystyle a^2-b^2=(a-b)(a+b)$

    2. $\displaystyle y^2-4x^2-20x-25=y^2-(2x+5)^2$ and use $\displaystyle a^2-b^2=(a-b)(a+b)$

    4. $\displaystyle 4y(y-3)^3(y+4)^4+6y(y-3)^5(y+4)^2=2y(y-3)^3(y+4)^2[2(y+4)^2+3(y-3)^2]$

    5. $\displaystyle \displaystyle\frac{1}{x}+\frac{1}{2}=\frac{x+2}{2x }$

    6. $\displaystyle \displaystyle \frac{3x}{4}+\frac{1}{2}=\frac{x}{3}-2$
    Multiply both sides by 12.

    7. $\displaystyle \displaystyle\frac{x}{x+2}=\frac{3x}{x-1}\Leftrightarrow x(x-1)=3x(x+2)$ and you continue.
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  3. #3
    Newbie
    Joined
    Sep 2007
    Posts
    2
    Thanks for the help, could you help me on these aswell or tell me the method to get the answer?

    1. $\displaystyle
    \frac{1}{x}+\frac{1}{y}+\frac{1}{w}
    $

    2. $\displaystyle
    5-\frac{3}{x}
    $

    3.
    $\displaystyle
    \frac{1}{x}+\frac{1}{y}
    $
    _____
    $\displaystyle
    \frac{1}{x}-\frac{1}{y}
    $

    4. $\displaystyle
    \frac{2}{x+1}+\frac{3}{x-1}
    $

    5. $\displaystyle
    \frac{1}{x+2}+5
    $

    6.
    $\displaystyle
    \frac{1}{x+2}+3
    $
    _________
    $\displaystyle
    2+\frac{1}{x+2}
    $

    7. $\displaystyle
    \frac{6x}{(x+2)(x+3)}-\frac{5}{(x+2)(x-3)}
    $
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  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
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    848
    Hello, chris123!

    Here is some help . . .


    $\displaystyle 3)\;\;\frac{\frac{1}{x}+\frac{1}{y}}{\frac{1}{x}-\frac{1}{y}} $
    Multiply top and bottom by $\displaystyle xy$:

    . . $\displaystyle \frac{xy\left(\frac{1}{x}+\frac{1}{y}\right)}{xy\l eft(\frac{1}{x} - \frac{1}{y}\right)} \;=\;\frac{y + x}{y - x}$



    $\displaystyle 6)\;\;\frac{\frac{1}{x+2}+3}{2+\frac{1}{x+2}}$
    Multiply top and bottom by $\displaystyle (x+2)$

    . . $\displaystyle \frac{(x+2)\left(\frac{1}{x+2} + 3\right)}{(x+2)\left(2 + \frac{1}{x+2}\right)} \;=\;\frac{1+3(x+2)}{2(x+2) + 1} \;=\;\frac{1 + 3x +6}{2x + 4+ 1} \;=\;\frac{3x+7}{2x+5}$



    $\displaystyle 7)\;\;\frac{6x}{(x+2)(x+3)}-\frac{5}{(x+2)(x-3)}$
    Get a common denominator . . .


    $\displaystyle \frac{6x}{(x+2)(x+3)}\cdot{\color{blue}\frac{x-3}{x-3}} \;- \;\frac{5}{(x+2)(x-3)}\cdot{\color{blue}\frac{x+3}{x+3}} \;\;= \;\;\frac{6x(x-3) \,- \,5(x+3)}{(x+2)(x+3)(x-3)}$

    . . $\displaystyle = \;\frac{6x^2-18x-5x-15}{(x+2)(x+3)(x-3)} \;\;=\;\;\frac{6x^2-23x - 15}{(x+2)(x+3)(x-3)}

    $

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