Answer
True.
Work Step by Step
Applying the quotient rule to the LHS:
$\displaystyle \quad \log_{b}(\frac{M}{N})=\log_{b}\mathrm{M}-\log_{b}\mathrm{N}$
$\displaystyle \log_{6}\left(\frac{x-1}{x^{2}+4}\right)=\log_{6}(x-1)-\log_{6}(x^{2}+4)$
Thus, the statement is true.
