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Math Help - Fractions

  1. #1
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    Fractions

    Can someone please help me with this?



    \frac{x}{1-\frac{1}{1-x}}




    Thank you!
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  2. #2
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    Krizalid's Avatar
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    Straightforward

     <br />
\mathcal A=\frac x{1-\dfrac1{1-x}}=\frac{1-x}{1-x}\cdot\frac x{1-\dfrac1{1-x}}

    So we have

    <br />
\begin{aligned}\mathcal A&=\frac{x(1-x)}{(1-x)-1}\\<br />
&=\frac{x(1-x)}{-x}\\<br />
&=\frac{x(x-1)}x\\<br />
&=x-1<br />
\end{aligned}<br />
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  3. #3
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    Thank you!
    But I don't understand, why do we multiply by 1-x ?


    Because I almost got to the same conclusion by using this method

    X:1-\frac{1}{1-x}


    then I multiplied 1*(1-x) to make the denominators the same.


    Then I followed the standard procedure for dividing fractions, in other words I multiplied x by the reciprocal \frac{1-x}{-x}


    and then I also got \frac{x(1-x)}{x}


    but then I don't understand, how one gets rid of the minus below?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Coach View Post
    Thank you!
    But I don't understand, why do we multiply by 1-x ?


    Because I almost got to the same conclusion by using this method

    X:1-\frac{1}{1-x}


    then I multiplied 1*(1-x) to make the denominators the same.


    Then I followed the standard procedure for dividing fractions, in other words I multiplied x by the reciprocal \frac{1-x}{-x}


    and then I also got \frac{x(1-x)}{x}


    but then I don't understand, how one gets rid of the minus below?
    Krizalid just applied a nice trick to clear the fractions in the denominator without actually combining them.

    note that he removed the minus in the denominator by changing the (1 - x) in the top to (x - 1)
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  5. #5
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    Quote Originally Posted by Jhevon View Post
    Krizalid just applied a nice trick to clear the fractions in the denominator without actually combining them.

    note that he removed the minus in the denominator by changing the (1 - x) in the top to (x - 1)

    Thank you!


    Does this method have a name so I can google it and learn it for further use?
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Coach View Post
    Thank you!


    Does this method have a name so I can google it and learn it for further use?
    i don't think so. the trick is to just multiply the top and bottom of the whole fraction by the common denominator of the fractions in the denominator of the big fraction
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  7. #7
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Coach View Post
    Thank you!


    Does this method have a name so I can google it and learn it for further use?
    Look up "complex fractions."

    -Dan
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