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Homework Help: Algebra help, Rational Equations

  1. Sep 30, 2013 #1
    1. The problem statement, all variables and given/known data

    Solving formulas involving Rational expressions
    for each excersise, solve for the indicated variable

    2. Relevant equations

    (x-y)/xy = z

    Solve for x

    3. The attempt at a solution

    I started by multiplying both sides by xy, to which I got

    (x-y) = xyz

    Then I tried multiplying both sides by yz

    (x-y)/yz = x

    And from there I just get stuck, I have tried everything I can think of, and I keep losing variables... I have done a bunch of other problems of the same type... and for some reason this one (the last one) has had me stuck for the past 45 minutes.

    Also, according to the back of the book, the answer is

    x = y/1-yz or x = -y/yz-1

    and even having the answers I can't figure out how to get there...

    Thank everyone for any help, I feel like I'm going to smack myself when I finally do figure it out.

  2. jcsd
  3. Sep 30, 2013 #2
    Hint: put terms with "x" one the one side of equation and terms without "x" on the other
  4. Sep 30, 2013 #3
    Thank you, I tried that. However, after I get:

    (x-y)/yz = x

    I can't seem to move the (x-y) without losing a variable somewhere, or, I could try backing up to step 2 and going to:

    (x-y)/x = yz

    Are either of these methods on the right track???


    Ok, I tried something else, which I feel is getting me closer,

    I started here as usual:

    x-y = (x)(y)(z)

    Then I moved the x from the left, over to the right, and the (y)(z) from the right to the left, giving me:

    -y/(y)(z) = x(-x)

    But then again, this could be moving in the wrong direction...
    Last edited: Sep 30, 2013
  5. Sep 30, 2013 #4


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    Homework Helper
    Education Advisor
    Gold Member

    You are on the right track but going off-track. You must concentrate on TERMS OF x, and get them all on one side, and everything else on the other side, and then you can finish in one step. Look back again on szynkasz's suggestion. That is really all you need.
  6. Sep 30, 2013 #5
    Mhorton91, how did you get:




    You can't divide one term on the right side by ##yz## and leave the other unchanged.
  7. Sep 30, 2013 #6
    when I had -y = (x)(y)(z)-x I divided both sides by (y)(z)

    Which gave me the -y/(y)(z) = (x) -x... is that not correct?
  8. Sep 30, 2013 #7
    Got it!!!

    x-y/xy = z

    x-y = xyz

    -y = (xyz - x)

    -y = x(yz-1)

    -y/(yz-1) = x

    Thank you for the hints!
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