Solving the Math Puzzle: Can't Follow Last Line

[DunWorry]

Homework Statement

I can't follow the math of the very last line.
It's really annoying me because I know its not supposed to be hard, I have tried multiplying top and bottom by k1+k2 and all kinds of rearranging but I'm not sure how they get from w1 - w2 / k1 - k2 = c (k1-k2) / (k1-k2)

Thanks

 

[Abhilash H N]

Given ω₁/k₁=c
and ω₂/k₂=c right?
On cross multiplying we'll get ω₁=ck₁ , ω₂=ck₂..
Put these values in (ω₁-ω₂)/(k₁-k₂) And take c outside the bracket so as to arrive at c(k₁-k₂)/(k₁-k₂) which on simplification gives c ...

 

[Ray Vickson]

Homework Statement

View attachment 61108

I can't follow the math of the very last line.
It's really annoying me because I know its not supposed to be hard, I have tried multiplying top and bottom by k1+k2 and all kinds of rearranging but I'm not sure how they get from w1 - w2 / k1 - k2 = c (k1-k2) / (k1-k2)

Thanks

They do not write
$$\omega_1 - \frac{\omega_2}{k_1} - k_2$$
as you claim. They write
$$\frac{\omega_1 - \omega_2}{k_1 - k_2}$$
which you can render in ASCII as (w1 - w2)/(k1-k2).