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Math Help - -Simplify Fractions-

  1. #1
    Junior Member fluffy_penguin's Avatar
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    Exclamation -Simplify Fractions-

    1) I'm at a loss of what to do here.


    2) Is this correct?


    3) Is this in lowest terms? Aka, did I do this right.


    4) Is this correct?


    5) Absolutely no clue. I'm probably going to have to ask my teacher monday how to do this because I'm so lost.
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  2. #2
    Member
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    1) \frac {3}{49z^3y}-\frac{1}{21z^2y}
    \implies \frac {3(21z^2y)-49z^3y}{(21z^2y)(49z^3y)}
    \implies \frac {63z^2y-49z^3y}{1029z^5y^2}
    \implies \frac {9z^2y-7z^3y}{147z^5y^2}
    \implies \frac {z^2(9y-7zy)}{147z^5y^2}
    \implies \frac {y(9-7z)}{147z^3y^2}
    \implies \frac {9-7z}{147z^3y}

    2) Correct.

    3) Correct.

    4) Correct.

    5) \frac{\frac{1}{x}+\frac{1}{y}}{\frac{x^2-y^2}{xy}}
    \implies\frac{\frac{x+y}{xy}}{\frac{x^2-y^2}{xy}}
    \implies\frac{x+y}{xy}\cdot\frac{xy}{x^2-y^2}
    \implies\frac{x+y}{x^2-y^2}
     <br />
\implies\frac{1}{x-y}<br />

    It's late so i might have made a mistake, please check.
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  3. #3
    Super Member
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    Quote Originally Posted by Sean12345 View Post
    1) \frac {3}{49z^3y}-\frac{1}{21z^2y}
    \implies \frac {3(21z^2y)-49z^3y}{(21z^2y)(49z^3y)}
    \implies \frac {63z^2y-49z^3y}{1029z^5y^2}
    \implies \frac {9z^2y-7z^3y}{147z^5y^2}
    \implies \frac {z^2(9y-7zy)}{147z^5y^2}
    \implies \frac {y(9-7z)}{147z^3y^2}
    \implies \frac {9-7z}{147z^3y}

    2) Correct.

    3) Correct.

    4) Correct.

    5) \frac{\frac{1}{x}+\frac{1}{y}}{\frac{x^2-y^2}{xy}}
    \implies\frac{\frac{x+y}{xy}}{\frac{x^2-y^2}{xy}}
    \implies\frac{x+y}{xy}\cdot\frac{xy}{x^2-y^2}
    \implies\frac{x+y}{x^2-y^2}
     <br />
\implies\frac{1}{x-y}<br />

    It's late so i might have made a mistake, please check.
    yeah thats correct!
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