How would you simplify (1+e^x) (1+e^ -x) - (1+e^x) (1-e^ -x) / (1+e^ x)^2?

Question

It is a question in Pre Calculus...It reads (One plus E raised to the X power) times (One plus E raised to the negative X power) MINUS (One pluse E raised to the X power) times (One minus E raised to the negative X power) DIVIDED by (One plus E raised to the X power) squared

Answer 1

Check the problem again. It doesn't simplify much ... I would have expected the terms with e^-x to either both be subtracted or added to one, not having the diferent signs you show.

It's not zero even how you have it written. If x=0, the result is (1+1)(1+1)- (1+1)(1-1)/(1+1)^2. Or 4 - 0 = 4. The answer isn't 4 either (for all x).

Answer 2

2/(1+e^x)

Answer 3

There are two terms in the expression separated by a minus sign (guess what minus sign it is). The denominator in the last expression maybe expanded so you can see what to cancel. Lets see:

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

Now you can cancel.

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

Answer 4

A=[(1+e^x+e^ -x+1)-(1+e^x-e^ -x-1)]/(1+e^x)^2
A=(2+2e^x)/(1+e^x)^2=2/(1+e^x)

Answer 5

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

Factor out 1 + e^x from the numerator
(1 + e^x)[1 + e^-x - (1 - e^-x)]/(1 + e^x)²

Cancel 1 + e^x from numerator and the denominator:
(1 + e^-x - 1 + e^-x)/(1 + e^x)

Combine like terms
2e^-x/(1 + e^x)

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Answer 6

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

Answer 7

Is that High School Work? I'm scared....(I start 10th grade in September)

Answer 8

easy enough, means meet me at the Y ( y because i love you) or it's between my l**gs

Answer 9

zero