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Math Help - Simplifying an expression

  1. #1
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    Simplifying an expression

    Can you please answer this question because i am getting lost ...

     \frac{x-y}{xy} +\frac{x-z}{xz}-\frac{z-y}{yz}
    Last edited by mr fantastic; February 21st 2009 at 12:59 PM. Reason: Moved to new thread - needed fixing.
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  2. #2
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    Quote Originally Posted by mj.alawami View Post

    Can you please answer this question because i am getting lost ...

     \frac{x-y}{xy} +\frac{x-z}{xz}-\frac{z-y}{yz}
    xyz is the LCD ...

     \frac{z(x-y)}{xyz} +\frac{y(x-z)}{xyz}-\frac{x(z-y)}{xyz}

    now finish
    Last edited by mr fantastic; February 21st 2009 at 01:00 PM.
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  3. #3
    Like a stone-audioslave ADARSH's Avatar
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    You can also follow



     <br /> <br />
=\frac{x}{xy} - \frac{y}{xy} + \frac{x}{xz} +\frac{-z}{xz} - \frac{z}{yz} - \frac{-y}{yz} <br />


    Now see if anything gets cancelled in

     <br />
=\frac{1}{y} - \frac{1}{x} + \frac{1}{z} +\frac{-1}{x} - \frac{1}{y} - \frac{-1}{z} <br />


    One more thing its always better to ask different questions in different threads
    Last edited by ADARSH; February 21st 2009 at 06:37 AM.
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  4. #4
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    Helli, mj.alawami!

     \frac{x-y}{xy} +\frac{x-z}{xz}-\frac{z-y}{yz}

    The LCD is xyz

    We must "convert" each fraction so they all have the LCD.
    . . We multiply each fraction by an appropriate fraction.

    {\color{blue}\frac{z}{z}}\cdot\frac{x-y}{xy} + {\color{blue}\frac{y}{y}}\cdot\frac{x-z}{xz} - {\color{blue}\frac{x}{x}}\cdot\frac{z-y}{yz}

    . . = \;\frac{z(x-y)}{xyz} + \frac{y(x-z)}{xyz} - \frac{x(z-y)}{xyz} .
    They have the same denominator.

    . . = \;\frac{z(x-y) + y(x-z) - x(z-y)}{xyz} .
    We can make one big fraction.

    . . = \;\frac{xz - yz + xy - yz - xz + xy}{xyz} .
    Simplify the numerator, factor, and reduce.

    . . = \;\frac{2xy - 2yz}{xyz} \;=\;\frac{2{\color{red}\rlap{/}}y(x-z)}{x{\color{red}\rlap{/}}yz} \;=\;\frac{2(x-z)}{xz}

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  5. #5
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    Quote Originally Posted by skeeter View Post
    xyz is the LCD ...

     \frac{z(x-y)}{xyz} +\frac{y(x-z)}{xyz}-\frac{x(z-y)}{xyz}

    now finish
    Attempt: [Is this correct ]
    <br />
\frac{-2zy+2xy}{xyz}=<br />
\frac{y(-2z+2x)}{y(xz)}=<br />
\frac{-2z+2x}{xz}<br />
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  6. #6
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    Quote Originally Posted by mj.alawami View Post
    Attempt: [Is this correct ]
    <br />
\frac{-2zy+2xy}{xyz}=<br />
\frac{y(-2z+2x)}{y(xz)}=<br />
\frac{-2z+2x}{xz}<br />
    look at Soroban's post ... is his final result the same as yours?
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