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Algebraic manipulation of equation

  1. Jun 8, 2014 #1
    Hi,

    I was wondering whether anyone could tell me how to deal with this manipulation, which I am unable to see.

    [tex]a_1=\frac{F}{(-m_1\omega^2+K_1+K_3)-K_3a_2}[/tex]

    [tex]a_2= \frac{K_3a_1}{(-m_2\omega^2 +K_2+K_3)}[/tex]

    Starting with [itex]a_1[/itex]:

    [tex]a_1=\frac{F}{(-m_1\omega^2+K_1+K_3)-\frac{K_3^2a_1}{(-m_2\omega^2 +K_2+K_3)}}[/tex]

    [tex]a_1(-m_2\omega^2 +K_2+K_3)=\frac{F(-m_2\omega^2 +K_2+K_3)}{(-m_1\omega^2+K_1+K_3)(-m_2\omega^2 +K_2+K_3) - K_3^2a_1}[/tex]


    The problem is I can't see how to eliminate [itex]a_1[/itex] from here... The result I need to get to is [tex]a_1=\frac{F(-m_2\omega^2 +K_2+K_3)}{(-m_1\omega^2+K_1+K_3)(-m_2\omega^2 +K_2+K_3) - K_3^2}[/tex]

    I know the steps are most likely simple and I'm missing something obvious but I can't see what it is that needs to be done (I'm a bit rusty, not having done any maths for a couple of months now)...

    Any advice would be much appreciated!
     
  2. jcsd
  3. Jun 8, 2014 #2
    Try making a quadratic equation in 'a 1' and solve it as usual.
     
  4. Jun 8, 2014 #3
    OK, thanks for the tip, Adithyan...
     
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