let's take 1 / (1 + e^(-2x)) first.

1 / (1 + 1/e^(2x))

1 / ((e^(2x) + 1) / e^(2x)) : see what i did here? i combined 1 and 1 / e^(2x) via least common denominator.

**e^(2x) / (e^(2x) + 1).**

now for e^(x) / (e^(x) + e^(-x)).

e^(x) / (e^(x) + 1 / e^(x))

e^(x) / ((e^(2x) + 1) / e^(x)) : again, i combined the e^(x) and the 1/e^(x) via least common denominator.

**e^(2x) / (e^(2x) + 1).**

the expressions are equal!

-slim