Question

(3^(n+2 )- 3^(n ))/(9^(n+1 )+ 9^(n-1 ) )

Answer 1

Oi :)

Segue a resposta

$\frac{3^{n+2}-3^n}{9^{n+1}+9^{n-1}}= \frac{3^{n}.3^2-3^n}{(3^2)^{n}.(3^2)^1+(3^2)^{n}:(3^2)^1}=\frac{3^{n}.(3^2-1)}{(3^n)^{2}.9+(3^n)^{2}:9}=\frac{3^{n}.(9-1)}{3^n(3^n.9+3^n:9)}= \\ \\ =\frac{8}{3^n.9+3^n:9} = \frac{8}{3^n(9+ \frac{1}{9} )}= \frac{8}{3^n. \frac{82}{9} } = \frac{8.9}{3^n.82 } = \frac{72}{82.3^n}= \frac{36}{41.3^n}$