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Math Help - [SOLVED] Proof - Can somebody please check my work

  1. #1
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    [SOLVED] Proof - Can somebody please check my work

    Hi,

    I am to prove the following:

    If a, b, c are real numbers s.t. a & c are NOT 0, then there is a unique number x s.t. x/a + b/c = 1.

    Ok, this is what I have:

    Let a, b, c be reals s.t. x/a + b/c = 1 and a & c are NOT 0.

    (x * 1/a) + (b * 1/c) = 1

    a[ (x*1/a) = 1 - (b * 1/c) ]

    x = a [ 1 - (b *1/c)]

    Since b*1/c is an element of R & 1-b/c is also and element of R,

    then a(1-b/c) is also an element of R.

    So x is an element of R.


    This seems pretty straight forward, but I just want to make sure that I am not approaching this wrong or am missing something in my proof. Thanks.
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  2. #2
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    That works as far as it goes. You have shown existence.
    Now show uniqueness: \frac{r}{a} + \frac{b}{c} = 1\,\& \,\frac{s}{a} + \frac{b}{c} = 1 \Rightarrow \quad r = s.
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  3. #3
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    will do! Thanks for help.
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