Find the domain of the first term, f1(x) = e((6x2+5x+1)/(2x-1)).

To find the domain of the function $f(x) = \log_e\left(\frac{6x^2+5x+1}{2x-1}\right) + \cos^{-1}\left(\frac{2x^2-3x+4}{3x-5}\right)$, we need to find the domain of each term and then take their intersection.

Step 1: Find the domain of the first term, $f_1(x) = \log_e\left(\frac{6x^2+5x+1}{2x-1}\right)$.
For the logarithm to be defined, its argument must be strictly positive:

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