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Math Help - algebra expression help

  1. #1
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    algebra expression help

    a,b,c and dare real numbers such that

     \frac{a}{b} = \frac{c}{d} and b does not equal d,
    show that

     \frac{a-c}{b-d} = \frac{a}{b}

    if i multiply by both sides by bd I get ad = bc so ad-bc = 0,

    thats as far as i can go..any help appreciated.


    thank you.
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  2. #2
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    Re: algebra expression help

    \dfrac{a-c}{b-d} = \dfrac{a}{b} if and only if b(a-c) = a(b-d) and b-d \neq 0 and b\neq 0. You know b-d \neq 0 since b \neq d and b \neq 0 since \dfrac{a}{b} \in \mathbb{R}.
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  3. #3
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    Re: algebra expression help

    Quote Originally Posted by Tweety View Post
    a,b,c and are real numbers such that
     \frac{a}{b} = \frac{c}{d} and b does not equal d,
    show that
     \frac{a-c}{b-d} = \frac{a}{b}
    Here is a slightly different way.
    From  \frac{a}{b} = \frac{c}{d} you can see that
    \\bc=ad\\-bc=-ad\\ab-bc=ab-ad\text{ adding }ab\\\text{ divide both by }b(b-d)
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