I am working my way through an astronomy equation.

given: a[t] = constant, single term

I'm as far as

z a[t] = 1 - a[t]

How does that evaluate to

1 + z + a[t] = 1

The (incorrect) way I see it is

given z a[t] = 1 - a[t]
add a[t] z a[t] a[t] = 1
simplify z a[t]^2 = 1
divide by a[t]^2 z = 1 / (a[t]^2)

I continue because the end is a(t) = 1 / (1+z)

I simply don't see where the second a[t] goes. Any help appreciated.

Question

I am working my way through an astronomy equation.  

given:  a[t] = constant, single term

I'm as far as 

z a[t] = 1 - a[t]

How does that evaluate to

1 + z + a[t] = 1

The (incorrect) way I see it is

given          z a[t] = 1 - a[t]
add a[t]      z a[t] a[t] = 1
simplify     z a[t]^2 = 1
divide by a[t]^2     z = 1 / (a[t]^2)

I continue because the end is a(t) = 1 / (1+z)

I simply don't see where the second a[t] goes.  Any help appreciated.

study312 · Answer

$\Huge\bigstar\color{#2E2EFE}{Welcome~to~OpenStudy!}\bigstar$ $\large\color{#01DFD7}{Made~by~Study312}$ if you would like to learn how to do what I just did you can see here http://openstudy.com/study#/updates/56afc9e0e4b01f7ec44daa26 and there are a lot more guides to LaTex in that topic room. Also, this is a newcomer openstudy guide http://openstudy.com/users/thesmartone#/updates/543de42fe4b0b3c6e146b5e8