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Phan Thanh Tinh Coordinator

04/09/2017 at 11:57
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Given the fraction \(\dfrac{x}{x-4}\) ( x is a digit). If we write the digit x to the right of the denominator, we get a new fraction which is equal to a. Find x if :

a) \(a=-\dfrac{3}{13}\)  b) \(a=\dfrac{1}{6}\)

Example : If x = 5, then \(x-4=1\) and \(a=\dfrac{5}{15}=\dfrac{1}{3}\)

If x = 2, then \(x-4=-2\) and \(a=\dfrac{2}{-22}=-\dfrac{1}{11}\)



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  • ...
    Dao Trong Luan 04/09/2017 at 13:14

    Suppose \(\dfrac{x}{x-4}\Rightarrow a=\dfrac{x}{\overline{x-4|x}}\)

    a, 

    a = \(-\dfrac{3}{13}=\dfrac{-3}{13}=\dfrac{3}{-13}\)

    \(\Rightarrow\left[{}\begin{matrix}x-4=1\\x-4=-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=5\\x=3\end{matrix}\right.\)

    Easy see x = 3 => a \(=-\dfrac{3}{13}\)

    So x = 3

    b,

    a = 1/6 

    => a - 4 \(\ge0\)

    => a > 4

    \(\Rightarrow5\le x\le9\)

    \(\Rightarrow1\le x-4\le5\)

    \(\Rightarrow a\in\left\{\dfrac{5}{15};\dfrac{6}{26};\dfrac{7}{37};\dfrac{8}{48};\dfrac{9}{59}\right\}\)

    Have 8/48 = 1/6

    So a = 8/48

    => x = 8

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  • ...
    Phan Thanh Tinh Coordinator 04/09/2017 at 13:34

    Dao Trong Luan's solution isn't logical at all. I need another one.



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