Rearranging terms in Trig equation

[PTX-14]

I was reading on planetary motion and have gotten hung up on a "rearrangement of terms" that the author skimmed over. It reads that:

r=e(k+rcos(θ))=(ek)/(1-ecos(θ))

It's been a while since I've been in a math class: I just can't follow how to get from a to b. Is there anyone who can walk me through this like I'm twelve?

Thanks!

 

[Nylex]

Put all the terms including $r$ on the left hand side and then factor out the $r$. It might help you to multiply out the brackets on the right hand side first:

\begin{equation}
r = e\left(k + r\cos \theta\right) = ek + er\cos \theta
\end{equation}

 

[uart]

Try getting all the "r" terms onto one side of the equation first. That is, try [strike]adding[/strike] subtracting $e\, r\, \cos(\theta)$ to both sides.

 

[Nylex]

That is, try adding $r\, e\, \cos(\theta)$ to both sides.

You mean subtracting, surely.

 

[uart]

You mean subtracting, surely.

Um yeah. Add the negative. ;)

BTW. We both posted at the same time. :)

 

[PTX-14]

Thank you two, I guess it's time for me to go back and audit some pre-algebra classes... :)