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Math Help - Prove this

  1. #1
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    Prove this

    Prove that if x is rational and x≠0, then 1/x is rational.
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  2. #2
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    Quote Originally Posted by ilovemymath View Post
    Prove that if x is rational and x≠0, then 1/x is rational.
    x is rational \displaystyle\Rightarrow\ x=\frac{a}{b}

    \displaystyle\frac{1}{x}=\frac{1}{\left(\frac{a}{b  }\right)}=\frac{\left(\frac{b}{b}\right)}{\left(\f  rac{a}{b}\right)}=\frac{\left(\frac{1}{b}\right)b}  {\left(\frac{1}{b}\right)a}
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  3. #3
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    why did you put (b/b)?
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  4. #4
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    Quote Originally Posted by ilovemymath View Post
    why did you put (b/b)?
    To get a common factor in both numerator and denominator.

    It helps to arrive at the final fraction since \frac{b}{b}=1 and \displaystyle\frac{\left(\frac{1}{b}\right)}{\left  (\frac{1}{b}\right)}=1

    You could also write

    \displaystyle\frac{1}{\left(\frac{a}{b}\right)}=\f  rac{b}{b}\frac{1}{\left(\frac{a}{b}\right)}=\frac{  b}{a}
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  5. #5
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    ya but eventually lets say a=1,b=2... at the end you will get the answer (1/(1/2)) and if u simplyfy is it will give u the anser 2... which is not rational
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  6. #6
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    Quote Originally Posted by ilovemymath View Post
    ya but eventually lets say a=1,b=2... at the end you will get the answer (1/(1/2)) and if u simplyfy is it will give u the anser 2... which is not rational
    2=\frac{2}{1}=\frac{4}{2}=\frac{6}{3}=.......

    2 is rational.
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  7. #7
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    ohhhk thnknss
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