Algebraic manipulation of equation

[jellicorse]

Hi,

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

$$a_1=\frac{F}{(-m_1\omega^2+K_1+K_3)-K_3a_2}$$

$$a_2= \frac{K_3a_1}{(-m_2\omega^2 +K_2+K_3)}$$

Starting with $a_1$:

$$a_1=\frac{F}{(-m_1\omega^2+K_1+K_3)-\frac{K_3^2a_1}{(-m_2\omega^2 +K_2+K_3)}}$$

$$a_1(-m_2\omega^2 +K_2+K_3)=\frac{F(-m_2\omega^2 +K_2+K_3)}{(-m_1\omega^2+K_1+K_3)(-m_2\omega^2 +K_2+K_3) - K_3^2a_1}$$


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

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!

 

[Adithyan]

Try making a quadratic equation in 'a ₁' and solve it as usual.

 

[jellicorse]

OK, thanks for the tip, Adithyan...