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Math Help - Simplifying with exponents

  1. #1
    Senior Member DivideBy0's Avatar
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    Simplifying with exponents

    Mr. Math Book says that

    \frac{e^x+e^{-x}}{e^x-e^{-x}}=\frac{e^{2x}+1}{e^{2x}-1}

    Can someone tell me how the LHS was simplified?? Thx
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  2. #2
    MHF Contributor red_dog's Avatar
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    \displaystyle \frac{e^x+e^{-x}}{e^x-e^{-x}}=\frac{e^x+\frac{1}{e^x}}{e^x-\frac{1}{e^x}}=\frac{\frac{e^{2x}+1}{e^x}}{\frac{e  ^{2x}-1}{e^x}}=\frac{e^{2x}+1}{e^{2x}-1}
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  3. #3
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    Hello, DivideBy0!

    Another way . . .


    \frac{e^x+e^{-x}}{e^x-e^{-x}}=\frac{e^{2x}+1}{e^{2x}-1}
    Multiply by \frac{e^x}{e^x}

    . . \frac{e^x}{e^x}\cdot\frac{e^x+e^{-x}}{e^x-e^{-x}} \;=\;\frac{e^{2x} + 1}{e^{2x} - 1}

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