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How to find the solutions of some fractional equations ?

  1. Sep 1, 2014 #1
    1. The problem statement, all variables and given/known data

    The problem is defined as below.

    A/B = x/y

    ; A/B and x/y are rational numbers.

    In some equations, we want to find solutions of variable x and y.
    A, B : given constants. integers.
    x, y : variables. integers.

    2. Relevant equations


    3. The attempt at a solution
     
  2. jcsd
  3. Sep 1, 2014 #2

    ShayanJ

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    Gold Member

    x=cA and y=cB for any c.
     
  4. Sep 1, 2014 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    For any integer c. But the point is that given any integers A and B, there are infinite pairs of integers x and y such that [itex]\frac{x}{y}= \frac{A}{B}[/itex].
     
  5. Sep 1, 2014 #4
    If you do that you should state something about the case ##c = 0##. The result that ##x = 0, y = 0, A = 1, B = 2## is probably not appropriate.
     
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