Precal: solve y = (e^x - e^(-x))/(e^x + e^(-x)) for x in terms of y

[mrnerd]

y = (e^x - e^(-x))/(e^x + e^(-x))

1. (e^x + e^(-x))y = (e^x - e^(-x)) /* I multiplied both sides by the denominator */

2. (e^2x + 1)y = e^2x - 1 /* I multiplied both sides to e^x to eliminate e^(-x) */

At this point I don't know what to do and I'm lost. Any help is much appreciated, thank you
-Evan

 

[Deleted member 4993]

y = (e^x - e^(-x))/(e^x + e^(-x))

1. (e^x + e^(-x))y = (e^x - e^(-x)) /* I multiplied both sides by the denominator */

2. (e^2x + 1)y = e^2x - 1 /* I multiplied both sides to e^x to eliminate e^(-x) */

At this point I don't know what to do and I'm lost. Any help is much appreciated, thank you
-Evan

Let:

e^2x = u

y = (u-1)/(u+1)

1 + y = (2u)/(u+1)....................(1)

1 - y = 2/(u+1)....................(2)

Divide (1) by (2) .............. and continue...............

 

[pka]

y = (e^x - e^(-x))/(e^x + e^(-x))

Look at this solution.

 

[mrnerd]

Thank you so much guys.