Answer
$e^{-3x}$
Work Step by Step
Use hyperbolic function formula as follows: $ \cosh x= \dfrac{e^x+e^{-x}}{2}$ and $ \sinh x= \dfrac{e^x-e^{-x}}{2}$
Need to solve: $\cosh (3x) - \sinh (3x)$
This implies: $\cosh (3x) - \sinh (3x)=\dfrac{e^{3x}+e^{-3x}}{2}-\dfrac{e^{3x}-e^{-3x}}{2}$
Hence, $\cosh (3x) - \sinh (3x)=e^{-3x}$
