Question

Evaluate:
$\frac{3\times {27}^{n+1}+9\times 3^{n-1}}{8\times 3^{3n}-5\times {27}^n}$

Answer 1

$\frac{3\times {27}^{n+1}+9\times 3^{n-1}}{8\times 3^{3n}-5\times {27}^n}=\frac{3\times {27}^n\times 27+9\times 3^{n-1}}{8\times 3^{3n}-5\times 3^{3n}}=\frac{3^{3n+4}+3^{n+1}}{3^{3n+1}}=3^3+3^{-2n}=27+\frac{1}{9^n}$