(A) Given expression: $\frac{2 \cdot 3^{n+1} + 7 \cdot 3^{n-1}}{3^{n+2} - 2 \cdot (3^{-1})^{1-n}}$$= \frac{2 \cdot 3^{n-1} \cdot 3^2 + 7 \cdot 3^{n-1}

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(A) Given expression: $\frac{2 \cdot 3^{n+1} + 7 \cdot 3^{n-1}}{3^{n+2} - 2 \cdot (3^{-1})^{1-n}}$$= \frac{2 \cdot 3^{n-1} \cdot 3^2 + 7 \cdot 3^{n-1}}{3^{n-1} \cdot 3^3 - 2 \cdot 3^{n-1}}$$= \frac{3^{n-1} (2 \cdot 9 + 7)}{3^{n-1} (27 - 2)}$$= \frac{18 + 7}{27 - 2}$$= \frac{25}{25} = 1$