SOLUTION: Could someone please show me the steps in solving this problem. (e^7x - e^-7x)^2 - (e^7x + e^-7x)^2 / (e^7x + e^-7x)^2 The book says that the answer is -4 / (e^7x + e^-7x)^2

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Could someone please show me the steps in solving this problem. (e^7x - e^-7x)^2 - (e^7x + e^-7x)^2 / (e^7x + e^-7x)^2 The book says that the answer is -4 / (e^7x + e^-7x)^2       Log On


   

Question 874623: Could someone please show me the steps in solving this problem.
(e^7x - e^-7x)^2 - (e^7x + e^-7x)^2 / (e^7x + e^-7x)^2
The book says that the answer is -4 / (e^7x + e^-7x)^2
I don't know how they got -4 for the numerator. I am getting something completely different.
Thanks in advance.
Found 2 solutions by mananth, rothauserc:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

use the identity a^2-b^2= (a+b)(a-b)



2e%5E%287x%29%2A-2%28e%5E%28-7x%29%29%2F%28e%5E%287x%29+%2B+e%5E%28-7x%29%29%5E2

=%28-4%29%2F%28e%5E%287x%29+%2B+e%5E%28-7x%29%29%5E2

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
e^14x -2 + (1/e^14x) - e^14x -2 - (1/e^14x) / (e^7x + e^-7x)^2
-4 / (e^7x + e^-7x)^2