Prove that: 1+e^z ---------=e^z 1+e^-z^ denotes power

We'll have to prove the identity (1+e^z)/(1+e^-z) =
e^z

We'll manage the left side and we'll
get:

(1+e^z)/(1+e^-z) =
(1+e^z)/(1+1/e^z)

We notice that we've used the negative
power property to write the term e^-z = 1/e^z

We'll
multiply 1 by e^z, within the brackets from
denominator:

(1+e^z)/[(e^z +
1)/e^z]

The fraction from denominator [(e^z + 1)/e^z] will
be reversed, such as:

(1+e^z)*e^z/(e^z +
1)

We'll simplify by (e^z + 1) and we'll
get:

(1+e^z)*e^z/(e^z + 1) =
e^z

We notice that managing the left side,
we'll get the expression form the right side, therefore, the identity (1+e^z)/(1+e^-z) =
e^z is verified.