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Simplify an equation

  1. Mar 25, 2009 #1
    i'm having trouble simplifying an equation.
    Basically it's in the form of [tex]1/A=B(1/C-1/D)[/tex]
    Now what i cant to do is solve for C.

    I get to [tex]1 = C(1/AB + 1/D)[/tex] but do not know where to go from there.

    Any help would be much appreciated, thanks.
     
  2. jcsd
  3. Mar 25, 2009 #2

    Integral

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    First of all we need to verify your starting equation, is it:

    [tex] \frac 1 A = B (\frac 1 C - \frac 1 D )[/tex]
     
  4. Mar 25, 2009 #3

    Mentallic

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    Yes you're nearly there.

    Let [tex]\frac{1}{AB}+\frac{1}{D}=x[/tex] so now we have [tex]1=Cx[/tex]

    What would you do at this point to solve (isolate the variable) for C?
     
  5. Mar 25, 2009 #4
    Yes intergral, that is the starting equation.

    Thanks Mentallic but i have a question.

    If i isolate the variable, C won't i get something like this:

    Let x be as you have stated. C = 1/x

    Now wouldn't the equation be C = 1/(1/AB + 1/D). Is this as far as i can go?
     
  6. Mar 25, 2009 #5

    Mentallic

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    Ok good, you've solved for C. However, it can be simplified further.

    Are you aware of the results:

    [tex]\frac{a}{b}+\frac{x}{y}=\frac{ay+bx}{by}[/tex] by finding the lowest common denominator?

    and

    [tex]\frac{1}{\left(\frac{a}{b}\right)}=\frac{b}{a}[/tex] ?

    Applying these two ideas, you'll be able to simplify the answer :smile:
     
  7. Mar 25, 2009 #6
    Thankyou.

    I used the equations that you gave me (forgotten high school maths) and was able to get:

    C = ABD/D+AB

    I hope this is correct?
     
  8. Mar 25, 2009 #7
    That's correct all right!
     
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