Attached is the question and possible solution. Is it correct?
Instead of writing e^(-x), try writing it as 1/(e^x). This should clarify it more.
Leave the denominator alone and just work with the numerator:
(e^x + 1/(e^x))(e^x + 1/(e^x)) - (e^x - 1/(e^x))(e^x - 1/(e^x))
Multiply out and you get:
e^2x +1 +1 + (1/(e^2x)) - [e^2x - 1 - 1 + (1/(e^2x))]
Simplify:
e^2x +2 + (1/(e^2x)) - e^2x +2 - (1/(e^2x))
which simplifies to:
4
So, in the end you have:
4 / (e^x + e^-x)^2
Hope this helps