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Math Help - Simplify this expression, is this correct?

  1. #1
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    Simplify this expression, is this correct?

    Attached is the question and possible solution. Is it correct?
    Attached Thumbnails Attached Thumbnails Simplify this expression, is this correct?-math.jpg  
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  2. #2
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    Response

    Instead of writing e^(-x), try writing it as 1/(e^x). This should clarify it more.
    Leave the denominator alone and just work with the numerator:
    (e^x + 1/(e^x))(e^x + 1/(e^x)) - (e^x - 1/(e^x))(e^x - 1/(e^x))

    Multiply out and you get:
    e^2x +1 +1 + (1/(e^2x)) - [e^2x - 1 - 1 + (1/(e^2x))]

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

    which simplifies to:
    4

    So, in the end you have:
    4 / (e^x + e^-x)^2

    Hope this helps
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  3. #3
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    Thanks!

    Just to clarify, on the denominator....you move the negative exponent down right so the final solution is actually:

    4/(e^x + (1/e^x))^2
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  4. #4
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    Response

    Yep. Either way is fine.
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