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Simple equation

  1. Mar 12, 2009 #1
    How can I solve this equation:

    [tex]
    \frac{1}{d^2} = \frac{1}{(9m)^2} + \frac{1}{(5m)^2}
    [/tex]

    ?

    Try:

    [tex]
    \frac{1}{d^2} = \frac{1}{81m^2} + \frac{1}{25m^2} \Rightarrow d^2 = 81m^2 + 25m^2 = 106m^2 \Rightarrow d = 10.3m
    [/tex]
     
  2. jcsd
  3. Mar 12, 2009 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    up to here you are fine. But
    is not true. if
    [tex]\frac{1}{a}= \frac{1}{b}+ \frac{1}{c}[/tex]
    it is NOT true that a= b+ c.
    More specifically,
    [tex]\frac{1}{\frac{1}{b}+ \frac{1}{c}}\ne b+ c[/tex]

    I recommend that you multiply both sides of the equation by the least common divisor of all three fractions, (25)(81)d2.
     
    Last edited: Mar 12, 2009
  4. Mar 12, 2009 #3

    Mark44

    Staff: Mentor

    Or even better, by (25)(81)d2m2
     
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