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Very hard algebra

  1. Dec 11, 2009 #1
    Well it's very hard for me anyway!
    In both of the following expressions I have to make x the subject. Can anybody break them down for me and explain step by step how to solve them?

    ax/b + cx/d = e

    a/bx + c/d = e

    From looking at the answers I know that the solutions are as follows:
    1. x = edb/ad+bc
    2. x = da/b(ed-c)
  2. jcsd
  3. Dec 11, 2009 #2


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    Gold Member

    I can give you a hint.

    For 1. start by using the distributive property
  4. Dec 11, 2009 #3
    So that would mean...
    - ax/b + cx/d = e
    - axd+cxb/bd = e
    and from there I can get to the answer x = edb/ad+bc by using and rearranging the formula A=BC/D. Is that the right way to do it?

    I've have tried applying the same logic to number and it doesn't seem to work.

    Thanks for your help by the way.
  5. Dec 11, 2009 #4


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    Science Advisor

    No; the above steps are incorrect. You've taken the term cx/d and multiplied top and bottom by b, which makes no difference to that term; but you've replaced ax/b with axd.

    The distributive property, in this case, means you should look for a common factor. This is a good way to approach problem number 1. The original equation is
    ax/b + cx/d = e

    Can you see any common factors there?

    Cheers -- sylas

    PS. Your solution to number 1 needs some parentheses.
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