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Math Help - Express rational function in terms of hyperbolic function

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    Express rational function in terms of hyperbolic function

    Hi! I'm new to this forum Please help with my math question!! Thanks heaps!

    Express the rational function [(16x^4)-1]/[(16x^4)+1] in terms of a hyperbolic function, logarithms and other functions as needed for x>0.

    ANS: tanh(2ln(2x)) for x>0
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    4x^2=e^t

    t=ln{4x^2}=2ln{2x}

    [(16x^4)-1]/[(16x^4)+1]=[(4x^2)-1/4x^2]/[(4x^2)+1/4x^2]=[(e^t)-e^(-t)]/[(e^t)+e^(-t)]=tanh{t}=tanh{2ln(2x)}
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    thanks a lot!!!
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