The value of 3 × 9^n + 1 + 9 × 3^2n - 19 × 3^2n - 6 × 9^n - 1 is equal to-

Answer: Option A

$$\begin{array}{rl}& \text{Expression}\\ & \frac{3\times 9^{n+1}+9\times 3^{2n-1}}{9\times 3^{2n}-6\times 9^{n-1}}\\ & =\frac{3\times {\left(3^2\right)}^{n+1}+3^2\times 3^{2n-1}}{3^2\times 3^{2n}-6\times {\left(3^2\right)}^{n-1}}\\ & =\frac{3^{2n+2+1}+3^{2n-1+2}}{3^{2n+2}-6\times 3^{2n-2}}\\ & =\frac{3^{2n+3}+3^{2n+1}}{3^{2n+2}-6\times 3^{2n-2}}\\ & =\frac{3^{2n+1}\left(3^2+1\right)}{3^{2n-2}\left(3^4-6\right)}\\ & =3^{2n+1-2n+2}\left(\frac{10}{75}\right)\\ & =\frac{3^3\times 10}{75}\\ & =\frac{27\times 10}{75}\\ & =\frac{18}{5}\\ & =3\frac{3}{5}\end{array}$$