Thread: 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

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)}

thanks a lot!!!