Help with this algebra involving e constants

I have this equation

(5/6) = (1-e^(-2k))/(1-e^(-4k)

and I'm suppose to solve for k

I thought that I would solve it like this:

(5/6) = (1-e^(-2k))/(1-e^(-4k) since a^b/a^c = a^b-c

(5/6) = (1+e^(2k))

In which I ended up getting k = ln(6) / 2

but when I checked the actual solution it was k = ln(5) / 2

What did I do wrong.

(5/6) = (1-e^(-2k))/(1-e^(-4k)
(1 - 1/e^(2k)) / (1 - 1/e^(4k)) = 5/6
(e^(2k) - 1) / e^(2k) / (e^(4k) - 1) / e^(4k) = 5/6
[e^(2k) * (e^(2k) - 1)] / (e^(4k) - 1) = 5/6
e^(2k)/ (e^(2k) + 1) = 5/6
6*e^(2k) = 5*e^(2k) + 5
e^(2k) = 5
k = ln(5) / 2

Edit where did you go wrong?
(5/6) = (1-e^(-2k))/(1-e^(-4k) since a^b/a^c = a^(b-c)
(5/6) = (1+e^(2k)) => here is your error, let's analyze:
let : e^(-2k) = a then we get:
(1 - a) / (1 - a^2) = 5/6
(1 - a)/[(1 - a)(1 + a)] = 5/6
1/(1 + a) = 5/6
5 + 5a = 6
5a = 1
a = 1/5 => sub.back for a = e^(-2k)
e^(-2k) = 1/5
e^(2k) = 5
k = ln(5) / 2

I hope this helps.