Difficult# An Application of Partial Fraction Decomposition

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Consider $f(t)=\cfrac{e^{3t}-e^{2t}+1}{e^{4t}-e^{2t}-2}$. This function is not a rational function.

However, we can simplify it using the techniques from the partial fraction decomposition.

The technique is to regard $e^t$ as a variable. Which of the following equals $f(t)$?