Question

(e^x)e^x+1)/(e^x-1)=8

Answer 1

I will assume you meant ...

(e^x)(e^x+1)/(e^x-1)=8
then
e^(2x) + e^x = 8e^x - 8
let e^x = y

y^2 - 7y + 8 = 0

I was hoping it would factor, check your typing

If it is correct it becomes a mess.
find y using the quadratic formula.
if you a negative answer, discard it since e^x cannot be negative
if y is positive, then
e^x = y
and x = ln y